ABSTRACT. An optical vortex is a light beam with a helically-shaped wavefront and a doughnut-like intensity. Such a beam carries an orbital angular momentum (OAM), which is quantized with a signed integer l related to the helix period. This quantum variable is also called the third momentum of light. We realized a vortex-conversion from red to blue using the 5S-5D two-photon transition in a rubidium vapor cell, monitored with a Gaussian beam at 780 nm plus a vortex beam at 776 nm with helicity l . The 5D level emission creates an infrared photon at 5.23 μm and a blue one at 420 nm. With a parallel co-propagating beam configuration, we demonstrate a high-helicity transfer, typically for l ranging -30 to +30, on the output blue beam which respects the OAM conservation. We further show that the output beam size respects the envelope of the input beams and that the conversion efficiency decreases with l, in respect with the input beams overlap. In addition we show the blue wave is a nearly pure Laguerre-Gaussian mode. That guaranties a high fidelity of the device viewed as an OAM transmitter and opens possibilities in the field of quantum variable manipulation for quantum communication.

ABSTRACT. Since its introduction in the 1930s by Wigner, and its generalisations by Moyal and Weyl, the ability to associate an operator on Hilbert space by a quasi-probability distribution function on phase space has found extensive use in the physics of continuous variable systems. Lacking, however, is finite system applications; to date, such functions have taken a back seat to state vector, path integration, and Heisenberg representations.

In recent work we have addressed this lack of application by generating a Wigner distribution function for any spin-j system or Dicke state in displaced parity form. Using this work, we have shown how varied quantum systems can be easily represented in phase space as well as visualise certain quantum properties, such as entanglement, within these systems. In particular, we have applied our formalism to directly measure phase space coordinates of multiple qubit states, including a five-qubit GHZ state, on IBM’s Quantum Experience. Applications to ions and photonics qubits have also been done.

ABSTRACT. We present a method to produce pure single photons with an arbitrary designed temporal shape in a heralded way. As an indispensable resource, the method uses pairs of time-energy entangled photons. One photon of a pair undergoes temporal amplitude-phase modulation according to the desired shape. Subsequent frequency-resolved detection of the modulated photon heralds its entangled counterpart in a pure quantum state. The temporal shape of the heralded photon is indirectly affected by the modulation in the heralding arm. We derive conditions for which the shape of the heralded photon is given by the modulation function. The method can be implemented with various sources of time-energy entangled photons. In particular, using entangled photons from parametric down-conversion the method provides a simple mean to generate pure shaped photons with an unprecedented broad range of temporal durations - from tenths of femtoseconds to microseconds. This shaping of single photons will push forward the implementation of scalable multidimensional quantum information protocols, efficient photon-matter coupling and quantum control at the level of single quanta.

ABSTRACT. Strongly interacting photons constitute a novel platform to study many-body physics and enable building blocks for quantum technologies. Photon-photon interaction being negligible in free space requires a medium to facilitate interactions. A single atom can absorb only one photon at a time and is therefore, in principle, well suited to couple simultaneously impinging photons. However, interactions between atoms and photons in the nonlinear regime at the single-photon level have been demonstrated only in the context of cavity quantum electrodynamics and Rydberg quantum optics.

Here we follow a conceptually simpler approach by tightly focusing the light field onto a single atom. Our implementation uses a 4Pi microscopy configuration: A single atom is placed between two lenses in a confocal arrangement. The incident beam is split, and the atom is coherently excited by two counter propagating parts of the field simultaneously. We observe 36% extinction of the incident field, and a modified photon statistics of the transmitted field – indicating nonlinear atom-photon interaction. Our results suggest, with 4Pi arrangement, free space implementation of atom-light interaction is strong enough to enter the regime of quantum nonlinear optics.

Reference: Y.-S. Chin, M. Steiner, C. Kurtsiefer, arXiv:1705.10173 (2017)

ABSTRACT. Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterise the output state by quantum state tomography; or alternatively to perform some kind of Bell test, tailored to the state of interest. We show here that neither approach is optimal amongst local verification strategies for two qubit states. We find the optimal strategy in this case and show that quadratically fewer total measurements are needed to verify to within a given fidelity than in quantum state tomography, Bell test, or fidelity estimation protocols. We also show that this quadratic advantage extends to any stabilizer state. The framework presented here is an indication that, in practice, devices for producing quantum states may be easier to verify than to characterise tomographically.

ABSTRACT. Quantum key distribution allows for the generation of a secret key between distant parties connected by a quantum channel such as optical fibre or free space. Unfortunately, the rate of generation of a secret key by direct transmission is fundamentally limited by the distance. This limit can be overcome by the implementation of so-called quantum repeaters. Here, we assess the performance of a specific but very natural setup called a single sequential repeater for quantum key distribution. We offer a fine-grained assessment of the repeater by introducing a series of benchmarks. The benchmarks, which should be surpassed to claim a working repeater, are based on finite-energy considerations, thermal noise and the losses in the setup. In order to boost the performance of the studied repeaters we introduce two methods. The first one corresponds to the concept of a cut-off, which reduces the effect of decoherence during storage of a quantum state by introducing a maximum storage time. Secondly, we supplement the standard classical post-processing with an advantage distillation procedure. Using these methods, we find realistic parameters for which it is possible to achieve rates greater than each of the benchmarks, guiding the way towards implementing quantum repeaters. arXiv:1705.00043

ABSTRACT. We show how adaptive protocols of quantum and private communication through bosonic Gaussian channels can be simplified into much easier block versions that involve resource states with finite energy. This is achieved by combining the adaptive-to-block reduction technique devised in [Pirandola et al., arXiv:1510.08863], based on teleportation stretching and relative entropy of entanglement, with the simulation of Gaussian channels introduced by [Liuzzo-Scorpo et al.,arXiv:1705.03017]. In this way, we derive weak converse upper bounds for the secret-key capacity of phase-insensitive Gaussian channel, which closely approximate the optimal limit for infinite energy. Our results apply to both point-to-point and repeater-assisted private communications.

ABSTRACT. We propose a scheme of loss resilient entanglement swapping between two distant parties in lossy optical fibre. In this scheme, Alice and Bob each begin with a pair of entangled non-classical states; these "hybrid states" of light are entangled discrete variable (Fock state) and continuous variable (coherent state) pairs. The continuous variable halves of each of these pairs are sent through lossy optical fibre to a middle location, where these states are then mixed (using a 50:50 beam-splitter) and measured. The detection scheme we use is to measure one of these modes via vacuum detection, and to measure the other mode using homodyne detection.

In this work we show that a maximally entangled Bell state can theoretically be produced following this scheme with high fidelity and entanglement, even when allowing for a small amount of loss. It can be shown that there is an optimal amplitude value of the coherent state when allowing for such loss. We also investigate the realistic circumstance when the loss is not balanced in the propagating modes. We demonstrate that a small amount of loss mismatch does not destroy the overall entanglement, thus demonstrating the physical practicality of this protocol.

(Ref: arXiv:1706.08492v1 [quant-ph])

ABSTRACT. As quantum key distribution (QKD) begins to move from laboratories into real-world use cases, some practical aspects need to be addressed before it can be widely adopted. Not least of which is the size and cost of the devices. The semiconductor industry, over the last 50 years, has provided a scalable platform for integrated electronics. Using the same fabrication processes, it is possible to create quantum photonic microchips to entirely replace the optical components needed for QKD. Using both indium phosphide and silicon devices, we can design and fabricate integrated devices to perform QKD with highly competitive speeds and error rates. At the same time, they offer dramatically reduced power requirements, size and costs while offering increased phase stability and inherent scalability. Other recent developments in the field include new protocols to remove the security assumptions about the physical devices used. One such protocol is measurement-device independent QKD (MDI-QKD) which removes all detector side-channels. Combining integrated devices with MDI-QKD, we are working towards developing a practical architecture for metropolitan QKD. Here, we provide a recap of QKD and discuss the current state of integrated QKD devices and their potential applications in metropolitan networks.

ABSTRACT. Quantum MAC allows two parties with a shared secret key to authenticate messages. The main advantage over classical MAC is that security of quantum MAC is guaranteed by laws of physics.

Formally [3], quantum MAC is a function that accepts a key and a (classical) input and outputs a (quantum) tag. Tags are different for different messages with the same key. To be different here means that inner product of states is small (states are near-orthogonal). The probability that given zero or more text-MAC pairs an arbitrary attacker would compute text-MAC pair for some new input is negligible.

We propose a quantum MAC based on the extractor against quantum storage [1]. This MAC is secure against an attacker that has the limited number of text-MAC pairs. We also propose a protocol that is based on this quantum MAC and we assess its security using the recently introduced notion of quantum information cost [2] and the notion of Holevo entropy.

[1] Ta-Shma, A. Short Seed Extractors Against Quantum Storage. Proc. ACM STOC 401–408 (2009). [2] Touchette, D. Quantum Information Complexity. Proc. ACM STOC 317–326 (2015). [3] Ziatdinov, M. From graphs to keyed quantum hash functions. Lobachevskii J. Math. 37, 705–712 (2016).

ABSTRACT. Quantum key distribution protocols have already been implemented in metropolitan networks all around the world. A promising method to provide the still missing long-haul link between such networks is optical satellite communication. To this end, existing Laser Communication Terminals (LCTs) can be adapted to be suitable for quantum communication. An important step towards this objective is to precisely characterize the quantum noise behaviour of the system including the channel. We have performed quantum-limited measurements of optical signals from the Alphasat TDP1 LCT in geostationary Earth orbit. We show that quantum coherence is preserved after propagation of the quantum states over 38600 km. An upper bound for excess noise that the states could have acquired after propagation is estimated [1].

Acknowledgements: The Laser Communication Terminal (LCT) and the Transportable Adaptive Optical Ground Station (T-AOGS) are supported by the German Aerospace Center (DLR) with funds from the Federal Ministry for Economic Affairs and Energy according to a decision of the German Federal Parliament.

References: [1] K. Günthner, I. Khan et al., "Quantum-limited measurements of optical signals from a geostationary satellite," Optica 4, 611 – 616 (2017).

ABSTRACT. Conference Key Agreement is an extension of Quantum Key Distribution to the N-partite scenario. We present a Device Independent Conference Key Agreement (DICKA) protocol, then we prove its security into two steps. We first use the recently developed Entropy Accumulation Theorem (by Dupuis et. al.) to split the overall min-entropy of Alice's string produced during the protocol, into a sum of the Von Neumann entropy produced in each round of the protocol (i.e. the sum of the entropy of each bit of the key). Then we develop a new method to bound the entropy produced in one round by a function of the violation of the N-partite Mermin-Ardehali-Belinskii-Klyshko (MABK) inequalities that generalizes the bounds found for the bipartite case. As far as we know this work is the first to provide a Device Independent security proof for Conference Key Agreement. We also show that DICKA can have some advantages over Device Independance QKD in certain regime of noise.

ABSTRACT. The complementarity principle is a tenet of our current understanding of quantum theory. In plain words it says that the sharpness of an interference pattern can be regarded as a measure of how wavelike the light is, and the amount of information we have obtained about the photons trajectories can be regarded as a measure of how particle-like it is.

Several theoretical papers have dealt with this subject and derived a quantitative relationship for the case of an interferometer. The most relevant experiment measures the interference of Rubidium atom trajectories in a double-slit configuration, and the path witness is the quantum internal state of the atoms, that change differently depending on the path taken by the atoms.

Here we demonstrate experimentally in an fully photonic interferometric system the relationship between the sharpness of interference (a measure of coherence, $G^{(1)}$), and the amount of trajectory information (a measure of degree of correlation, $G^{(2)}$). We show in this way in an experiment the relevant and fascinating interplay between quantum coherence and quantum correlations.

ABSTRACT. The Hilbert space dimension of a quantum system is the most basic quantifier of its information content. Lower bounds on the dimension can be certified in a device-independent way, based only on observed statistics. We highlight that some such ``dimension witnesses'' capture only the presence of systems of some dimension, which in a sense is trivial, not the capacity of performing information processing on them, which is the point of experimental efforts to control high-dimensional systems. In order to capture this aspect, we introduce the notion of irreducible dimension of a quantum behaviour. This dimension can be certified, and we provide a witness for irreducible dimension four. Based on arXiv:1611.01258

ABSTRACT. Although an input distribution may not majorize a target distribution, it may majorize a distribution which is close to the target. Here we introduce a notion of approximate majorization. For any distribution, and given a distance $\delta$, we find the approximate distributions which majorize (are majorized by) all other distributions within the distance $\delta$. We call these the steepest and flattest approximation. This enables one to compute how close one can get to a given target distribution under a process governed by majorization. We show that the flattest and steepest approximations preserve ordering under majorization. Furthermore, we give a notion of majorization distance. This has applications ranging from thermodynamics, entanglement theory, and economics.

ABSTRACT. The violation of Bell inequalities allows the certification of quantum properties in a device-independent way [1]. This means that random numbers [2] or the security of a secret key [3] can be guaranteed, without any assumptions on the internal functioning of the devices used in the protocol. Given the task of certifying random numbers, one can see entanglement as a resource, in the sense one can study the amount of random bits that can be extracted from various entangled quantum states. The relation between entanglement and randomness was studied in [4] and turned out to be more complex than expected. For the maximally entangled state, it is known that maximal randomness of 2 bits can be certified [5]. In our work, we develop a family of Bell inequalities to certify maximal randomness from partially entangled states of two qubits.

[1] - N. Brunner et al., Rev. Mod. Phys. 86, 419 (2014). [2] - S. Pironio et al., Nature 464, 1021 (2010). [3] - A. Acin et al., Phys. Rev. Lett 98, 230501 (2007). [4] - A. Acin, et al., Phys. Rev. Lett. 108, 100402 (2012). [5] - C. Dhara, et al., Phys. Rev. A 88, 052116 (2013).

ABSTRACT. Quantum teleportation, the process by which Alice can transfer an unknown quantum state to Bob by using pre-shared entanglement and classical communication, is one of the cornerstones of quantum information. The standard benchmark for certifying quantum teleportation consists in surpassing the maximum average fidelity between the teleported and the target states that can be achieved classically. According to this figure of merit, not all entangled states are useful for teleportation. Here we propose a new benchmark that uses the full information available in a teleportation experiment and proves that all entangled states can implement a quantum channel which can not be reproduced classically. We introduce the idea of non-classical teleportation witness to certify if a teleportation experiment is genuinely quantum and discuss how to quantify this phenomenon. Our work provides new techniques for studying teleportation that can be immediately applied to certify the quality of quantum technologies.

ABSTRACT. Gedankenexperiment have been conceived to inspect the counterintuitive principles of quantum mechanics, for example, the wave-particle duality. Wheeler proposed his delayed-choice thought experiment to test the validity of the dual description of photons and to highlight the naive and contradictory interpretation given by classical physics: by changing the configuration of a two-path interferometer after the photon has entered the setup, one can either investigate the particle-like nature of the photon or its wave-like behavior. Motivated by the need of testing quantum mechanics in new scenarios, we implemented the delayed-choice experiment along a satellite-ground interferometer which extends for thousands of kilometers in Space allowing us to probe the laws of nature at this unprecedented scale. We exploit temporal and polarization degrees of freedom of photons reflected by a fast moving satellite equipped with retro-reflecting mirrors. Our results extend the validity of the quantum complementarity to the scale of Low Earth Orbits, paving the way for novel applications of quantum information processing in Space links involving multiple photon degrees of freedom. Furthermore, our experiment is a workbench for the development of new quantum technologies and techniques that enable the ability of propagating and controlling quantum phenomena over increasingly larger distances.

ABSTRACT. One of the big questions about quantum theory since its early days is asking whether entanglement as one of the fundamental quantum phenomena persists also in macroscopic systems. Nowadays the measurement of large-scale entanglement is still a hard problem. To witness entanglement we use the concept of entanglement depth defined by the system’s minimal number of mutually entangled atoms.

The entanglement witness used in this work is based on the coherent superposition of a single excitation shared by many atoms. Previous measurements lead to entanglement of up to 2900 particles. Our experiment witnesses genuine multipartite entanglement between 16 millions of atoms in a solid-state quantum memory even in the presence of loss and noise.

The experiment consists of two steps: 1. Entanglement appears in a quantum memory realized by a Nd:YSO crystal during the storage of the single photon excitation. 2. The read-out measurements are based on the photon counts and the second-order auto-correlation function concluding on the system’s entanglement depth for given system size.

The resulting raw data lead directly to an entanglement depth of half a million. Inferring the photon probabilities for perfect detectors, the entanglement depth is as high as 16 millions.

ABSTRACT. Batteries operating on quantum scale are of huge interest nowadays. We investigate the process of charging a quantum battery, a system represented by two qubits in our work. These two qubits define a four-level system from the energetic point of view. We use incoherent quantum states as the initial state of our battery, manipulated by filtering procedures. The filtering operation consists of application of projective measurement and subsequent conditioning on certain outcome of the measurement. Applying filtering procedures to different levels of the system, we find that filtering out the ground state gives us increase in the energy of the system, which is analogous to the process of charging the battery. Moreover, for some values of the relevant parameters of the system, the entropy of the battery is decreased as well, compared to the initial state. We compare the results obtained for the incoherent initial states of the battery with those obtained from the filtering procedure applied to the pure initial quantum states of the battery.

ABSTRACT. Being able to successfully implement quantum information processing in practice hinges on the reliable generation of entanglement, which remains a challenge for even the most modern experimental techniques. Contrary to the usual approach of shielding the quantum system from its environment, dissipative techniques attempt to deliberately incorporate dissipation into the system dynamics, inherently stabilising it against detrimental effects of the environment. The feasibility of generating steady state entanglement between two trapped beryllium ions, by utilising a dissipative mechanism, has been experimentally demonstrated [1]. Ultimately, the success of the above approach is hampered by limitations associated with its particular implementation. We therefore propose two modifications to the original beryllium ion scheme, leading to improved entanglement whilst respecting current experimental limitations. Optimising the polarisation of the laser beams utilised in the experiment is a first step towards improvement of the entanglement fidelity. More significantly, it is possible to drive alternate combinations of transitions between internal states of the beryllium ions. We have found a specific combination of transitions, which when combined with optimised polarisation, enables both faster entanglement and an increase in the attained fidelity by an order of magnitude. [1] Lin Y. et al. Nature 504, 415 (2013)

ABSTRACT. A streaming algorithm is a well-known computational model that has a relationship with automata and branching programs models. We consider a quantum version of streaming algorithms for solving online minimization problems (OMP). It is the first time when quantum streaming algorithms are explored for solving such problems. And we also can consider this model as a quantum online algorithm with restricted memory. In the paper, we show that quantum streaming algorithms for OMP can be better than classical ones (deterministic or randomized) for sub-logarithmic and poly-logarithmic space (memory), and they can be better than deterministic online algorithms without restriction for memory.

Another point of view to the online algorithms model is advice complexity. So, we introduce quantum online algorithms with a quantum channel with an adviser. Firstly, we show that quantum algorithms have at least the same computational power as classical ones have. Secondly, we consider quantum online algorithms that share entangled qubits with an adviser. We show that these algorithms can use twice less advise qubits comparing to classical counterparts.

ABSTRACT. We consider the quantum dynamics of a non-relativistic free particle moving in a cavity and we analyze the effect of a rapid switching between two different boundary conditions. We show that this procedure induces, in the limit of infinitely frequent switchings, a new effective dynamics in the cavity related to a novel boundary condition. We explicitly compute the novel boundary condition in terms of the two initial ones. With this procedure we define a dynamical composition law for boundary conditions.

ABSTRACT. Objectivity constitutes one of the main features of the macroscopic classical world. An important aspect of the quantum-to-classical transition issue is to explain how such a property arises from the microscopic quantum world. Recently, within the framework of open quantum systems, such a mechanism has been proposed in terms of the, so-called, Spectrum Broadcast Structures. These are multipartite quantum states of the system of interest and a part of its environment, assumed to be under an observation. This approach requires a departure from the standard open quantum systems methods, as the environment cannot be completely neglected. Here we study the emergence of such a state-structures in one of the canonical models of the condensed matter theory: Spin-boson model. We pay much attention to the behavior of the model in the non-Markovian regime, in order to provide a testbed to analyze how the non-Markovian nature of the evolution affects the creation of a spectrum broadcast structure.

ABSTRACT. Due to its high sensitivity to small magnetic fields at room temperature, the nitrogen-vacancy center (NV center) in diamond is a promising tool for resonance imaging of single electron spins in molecules using atomic force microscopy (AFM) techniques under ambient conditions. Using the spin-labels in molecules, the only limitation in imaging single spins in molecules with the NV center, is the spatial resolution. Every electron spin in resonance with the measurement scheme contributes to the signal and thereby reduces the probability of detecting single spins. The aim of this work is to spatially restrict the number of resonant electron spins by using a strong magnetic field gradient. Since strong off -axis magnetic fields disturb the optical readout of the NV center spin state, we try to fabricate magnetic tips with low total magnetic field strength but with a gradient in the range of 10G/nm. Commercially available magnets, like AFM tips, do not generate such fields. This work is split up into three steps, first the micromagnetic simulation of the required geometry, secondly the fabrication of high gradient magnetic on tips and finally the integration of such tips into an AFM setup for easurements with an NV center.

ABSTRACT. A watched quantum arrow does not move. This effect, referred to as the quantum Zeno effect, arises from a frequent measurement of a quantum system’s state. In more general terms, the evolution of the quantum system can be confined to a subspace of the system’s Hilbert space leading to quantum Zeno dynamics. Resulting from the measurement process, a source of dissipation is introduced into the systems dynamics. However, different than for a common open quantum system, we can choose the strength of the dissipation by changing the parameters of the Zeno measurement. We capitalise on the property of tunable dissipation to create a quantum simulator for open quantum systems. Due to the formal analogy of the measurement process and the theory of open quantum systems, we can derive a Lindblad master equation to describe the evolution of the open quantum system. Moreover, we extend the picture to enable also non-Markovian evolution in the quantum simulator. The considered quantum system are photons inside a cavity being subject to a indirect measurement using circular Rydberg atoms. The setup is inspired by Zeno experiments proposed in the framework of cavity quantum electrodynamics [1]. [1] Raimond et al. Phys. Rev. A 86, 032120 (2012)

ABSTRACT. Using the variance based uncertainty, we introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty and show that conditioning on more observable reduces the uncertainty. Given three observables, we prove a ‘strong sub-additivity’ theorem for the conditional uncertainty under certain condition. As an application, we show that for pure product two-qubit states, the mutual uncertainty is bounded by 0.586 and if it is greater than this value then it indicates that the state is entangled. For mixed two-qubit states, we prove that the mutual uncertainty for product, classical-classical, and classical-quantum state also takes a universal value 0.586. We also show how to detect quantum steering using the mutual uncertainty between two observables. Our results may open up a new direction of exploration in quantum theory and quantum information using the mutual uncertainty, conditional uncertainty and the strong sub-additivity for multiple observables.

ABSTRACT. We trap atomic ensembles in a two-dimensional array of Ioffe-Pritchard type magnetic microtraps above an atom chip, with the goal of inducing interaction between Rydberg atoms. Due to adsorbate Rb atoms on the chip Rydberg excitations are shifted and broadened due to stray electric fields. We use Rydberg spectroscopy to measure these electric fields and gradients, and their dependence on the distance to the surface [1]. We also demonstrate a method to control electric fields by mild local heating using the blue Rydberg excitation laser, which changes the distribution of adsorbed atoms on the silica layer. This method allows us to reduced the stray electric to less than 2 V/cm at 61 um distance. [1] J. Naber et al., J Phys B, Vol.49 N. 9 (2016)

ABSTRACT. We study the state evolution of the fields produced by classical sources, when recording intensity correlations of higher order in a generalized Hanbury Brown and Twiss setup [1,2]. Apart from an offset, we find that the angular distribution of the last detected photon is identical to the superradiant emission pattern generated by an ensemble of two-level atoms in entangled symmetric Dicke states. As a consequence, we demonstrate that the Hanbury Brown and Twiss effect, originally established in astronomy to determine the dimensions or separation of stars, and Dicke superradiance, commonly observed with atoms in highly entangled Dicke states, are two sides of the same coin. We show that the phenomenon derives from projective measurements induced by the measurement of photons in the far field of the sources and the permutative superposition of quantum paths identical to those leading to superradiance in the case of single photon emitters [3]. [1] S. Oppel, et al., Phys. Rev. Lett. 113, 263606 (2014). [2] D. Bhatti, et al., Phys. Rev. A 94, 013810 (2016). [3] R. Wiegner, et al., Phys. Rev. A 92, 033832 (2015).

ABSTRACT. In a Bell experiment, certain extremal correlations (summarized in the Bell value) between the joint input and output of the players almost uniquely identify the quantum state they share. This phenomenon is known as self-testing and has applications in quantum cryptography with untrusted devices. For practical applications, self-testing statements need to be robust to noise.

We extend previous work on self-testing of pure two-qubit states. First, we use a family of Bell inequalities called tilted CHSH inequalities to improve the robustness of previously found self-testing statements for (almost) all pure partially-entangled two-qubit states. Our result is obtained using a recently developed method of deriving self-testing statements from operator inequalities.

Furthermore, we construct a bipartite state with the following two properties: (a) it violates the CHSH inequality, and (b) there exist no local quantum channels that the two players could apply to their state to achieve greater singlet fidelity than a trivial lower bound (i.e. the singlet fidelity achievable using a separable state). This result implies that there exists a threshold violation below which the players cannot `extract' a singlet from their state by just local operations.

Future research will focus on extending our results to GHZ-states and on quantum steering.

ABSTRACT. Laser cooling is a widely used technique in experiments in quantum optics and information. For the most purposes of cooling above the Doppler limit laser fields are used which can be modelled by plane running waves. In this regime, the interaction between electromagnetic field and particles, modelled as two level systems, is well explained by the semiclassical theory of Doppler cooling. Nevertheless, already in the semiclassical regime standing waves give rise to different cooling properties as in the running wave case[Ci92]. Experiments conducted in Erlangen investigate the coupling between the electromagnetic field and a trapped particle near the focus of a parabolic mirror. Around the focus, the reflected and focused field mimics the time-inverted mode pattern of a spontaneous decay which enhances the excitation probability. In this setup, interactions of strongly focused standing waves with the trapped particle have to be considered. We developed a semiclassical theory which, in contrast to the usual theory of Doppler cooling, includes both. We will present stochastic simulations of the steady states of the particle distribution inside the parabolic mirror for different field intensities and simulations of saturation measurements which can be compared with experiments.

[Ci92] Cirac et.al,Phys.Rev.A,Vol.46,No.5,Sep 1992,2668-2681

ABSTRACT. We distilled different definitions of entanglement of identical particles from works discussed in quantum information literature. We compare them on the basis of some physical principles. One is that entanglement, as any physical correlation between particles, cannot be created by local operations, in physical terms without interactions. The second principle is that the theory of entanglement of identical particles must be consistent with the theory for distinguishable particles, when the physical description of the latters effectively emerge from the framework of identical particles, e.g. when identical particles are effectively distinguished by means of unambiguous properties. The last requirement is that, in the absence of other genuinely quantum effects, entanglement captures quantum enhanced performances in information processing. We find that the only notion of entanglement that is fully consistent with the above principles is the so-called mode-entanglement, e.g. entanglement between modes in the Fock space, which is in turn an application of a more general framework where entanglement is defined through non-classical correlations between subalgebras of observables.

ABSTRACT. We introduce a new feature of no-signaling (Bell) non-local theories, namely, when a system of multiple parties manifests genuine non-local correlation, then there cannot be arbitrarily high non-local correlation among any subset of the parties. We call this feature, \textit{complementarity of genuine multipartite non-locality}. We use Svetlichny's criterion for genuine multipartite non-locality and non-local games to derive the complementarity relations under no-signaling constraints. We find that the complementarity relations are tightened for the much stricter quantum constraints. We compare this notion with the well-known notion of \textit{monogamy of non-locality}. As a consequence, we obtain tighter non-trivial monogamy relations that take into account genuine multipartite non-locality. Furthermore, we provide numerical evidence showcasing this feature using a bipartite measure and several other well-known tripartite measures of non-locality.

ABSTRACT. We study the communication complexity of computing a function f in expectation. This requires Alice and Bob on inputs x and y respectively to output a nonnegative number whose expectation is f(x,y). The goal is to use as little communication as possible. It is known in literature that the number of classical bits needed is exactly characterised by the logarithm of the non-negative rank of the communication matrix. Similarly, the number of qubits that needs to be communicated is characterised by the logarithm of the positive-semidefinite rank of the communication matrix. We call protocols 'mixed' if we allow classical bits followed by qubits to be communicated during the protocol. We introduce a notion of rank and exactly characterise the communication complexity in expectation for mixed protocols using this rank.

We also study the correlation generation problem, where we have two random variables X and Y and Alice and Bob have to sample values from X and Y according to their joint probability distribution. We again use the above notion of rank to characterise the amount of information in terms of the number of bits and qubits that must be communicated for a mixed protocol to generate a given correlation.

ABSTRACT. We have designed efficient quantum circuits for the three-qubit Toffoli (controlled-controlled NOT) and the Fredkin (controlled-SWAP) gate, optimized via genetic programming methods. The gates thus obtained were experimentally implemented on a three-qubit NMR quantum information processor, with a high fidelity. Toffoli and Fredkin gates in conjunction with the single-qubit Hadamard gates form a universal gate set for quantum computing and are an essential component of several quantum algorithms. Genetic algorithms are stochastic search algorithms based on the logic of natural selection and biological genetics and have been widely used for quantum information processing applications. The numerically optimized rf pulse profiles of the three-qubit quantum gates achieve >99% fidelity. The optimization was performed under the constraint that the experimentally implemented pulses are of short duration and can be implemented with high fidelity. Therefore the gate implementations do not suffer from the drawbacks of rf offset errors or debilitating effects of decoherence during gate action. We demonstrate the advantage of our pulse sequences by comparing our results with existing experimental schemes.

ABSTRACT. Entanglement is a crucial resource in quantum communication, but producing entanglement in a quantum network is generally a costly process. It would therefore be useful if already existing entanglement in the network can be recycled. Consider for example the case where a subset of the parties in the network wish to run some protocol, for example a secret sharing or anonymous transfer protocol, which requires a GHZ-state shared between these parties. A natural question is then whether this GHZ-state can be produced from the current state in the network, by performing local operations.

In this work we focus on transforming graph states by local Clifford operations and local Pauli measurements. In particular we consider the question of whether a graph state, the target state, can be reached from some original graph state, using these local operations. It is already well know how to efficiently decide if two graph states are equivalent under local Clifford operations. However it is not know how to do this if also local Pauli measurements are included. We solve this problem for a subclass of graphs and present an efficient algorithm that works when the target state is a GHZ-state and the original graph is distance-hereditary.

ABSTRACT. The accurate simulation of molecular systems is one of the great promises of the coming age of quantum computers. With small scale quantum computers beginning to emerge, this goal appears to be close at hand. However, many challenges remain. One of them is the high number of qubits required for simulating molecules in the formalism of second quantization: a problem that is quite severe for state-of-the-art quantum processors. In this work, we develop methods that allow us to trade qubit resources for algorithmic complexity. The main idea behind our efforts is to encode molecular configurations as quantum states, where the amount of qubits required is reduced by accounting for Hamiltonian symmetries like particle number conservation. For that purpose, different codes are introduced that eliminate a constant, linear and exponential amount of qubits with respect to the system size. For any code in general, it is demonstrated how to transform operators of the molecular Hamiltonian into gate sequences. We expect our work to be relevant for near-term quantum simulation experiments, but also in the longer term as logical qubits are expected to remain a scarce resource for the foreseeable future.

ABSTRACT. The generation and manipulation of high-dimensional entangled states of light on a miniaturized chip is a cornerstone for quantum information technologies [1]. Among the different platforms under study, AlGaAs-based devices attract a considerable interest thanks to their compliance with electrical injection [2] and electro-optic effect. Here we demonstrate AlGaAs waveguides emitting photon pairs with a high rate (2.37MHz) and a signal-to-noise ratio up to 5e4. This result potentially brings us in the condition of achieving a 0.99 fidelity to a maximally entangled state. Our devices are based on a modal phase-matching scheme and emit orthogonally polarised twin photons at 1560nm. The dispersion properties of our devices, together with the modal reflectivity on the waveguide facets, lead to the generation of a biphoton state with a comb-like joint spectral amplitude, corresponding to frequency-entangled Qudits. The emission of an entangled Qudit state is supported by the measurements of the Joint Spectral Intensity and Hong-Ou-Mandel interference. Contrary to recent experiments requiring external filter or cavities to engineer the target state, our devices represent a miniaturized source, working at room temperature and telecom wavelength. [1] M. Kues et. al., Nature 546, 622-626, (2017) [2] F. Boitier et al., Phys. Rev. Lett 112, 183901, (2014)

ABSTRACT. We derive from first principles the momentum exchange between a photon and a quantum mirror upon reflection, by considering the boundary conditions imposed by the mirror surface on the photon wave equation. We show that the system generally ends up in an entangled state, unless the mirror position uncertainty is much smaller than the photon wavelength, when the mirror behaves classically. Our treatment leads us directly to the conclusion that the photon momentum has the known value h/λ. This implies that when the mirror is immersed in a dielectric medium the photon radiation pressure is proportional to the medium refractive index n. Our work thus contributes to the longstanding Abraham-Minkowski debate about the momentum of light in a medium. We interpret the result by associating the Minkowski momentum (which is proportional to n) with the canonical momentum of light, which appears naturally in quantum formulations. DOI: https://doi.org/10.1103/PhysRevA.93.023803

ABSTRACT. Possibility of generating several nonclassical states various optical systems, such as nonlinear optical couplers [1,2] and hyper-Raman process [3], is studied. Specifically, the presence of nonclassical states is investigated in an asymmetric nonlinear optical coupler, composed of one linear and one nonlinear ($\chi^{2}$) waveguides, for both codirectional [1] and contradirectional [2] propagation of fields. Additionally, most general form of hyper-Raman process is also studied [3]. Interestingly, both lower and higher order squeezing, antibunching and entanglement have been observed in all cases. Further, quantum Zeno and anti-Zeno effects are observed in the symmetric [4] (with both nonlinear ($\chi^{2}-\chi^{2}$) waveguides) optical couplers. A completely quantum mechanical model has been used to describe all the systems considering all the field modes involved to be weak. Heisenberg's equations of motion for all the modes are obtained and Sen-Mandal perturbative technique was used to obtain closed form analytic expressions of evolution of all the field modes [1-4].

[1] K. Thapliyal, et al., Phys. Rev. A 90, 013808 (2014).

[2] K. Thapliyal, et al., Phys. Lett. A 378, 3431 (2014).

[3] K. Thapliyal, et al., Nonclassicality in hyper-Raman process, Communicated (2017).

[4] K. Thapliyal, et al., Phys. Rev. A 93, 022107 (2016).

ABSTRACT. We present a new method for evaluating the response of a moving qubit detector interacting with a scalar field in Minkowski spacetime. We treat the detector as an open quantum system, but we do not invoke the common Markov and Rotating Wave approximations. The evolution equations for the qubit density matrix are valid at all times, for all qubit trajectories, and they incorporate non-Markovian effects. We analyze in detail the case of uniform acceleration, providing a detailed characterization of all regimes where non-Markovian effects are significant. We argue that the most stable characterization of acceleration temperature refers to the late time behavior of the detector because interaction with the field vacuum brings the qubit to a thermal state at the Unruh temperature. In contrast, the early-time transition rate, that is invoked in most discussions of acceleration temperature, does not exhibit a thermal behavior when non-Markovian effects are taken into account. Furthermore, we note that the non-Markovian evolution derived here also applies to the mathematically equivalent problem of a static qubit interacting with a thermal field bath. Finally, we discuss the implications of our results for the treatment of a moving qubit interacting with an electromagnetic field.

ABSTRACT. The size of quantum computing systems is set to increase rapidly in the near term future. Recently we made a proposal for a large scale quantum processor to be implemented in silicon quantum dots. This system features a crossbar control architecture which limits parallel single qubit control, but allows the scheme to overcome scaling issues that form a major hurdle to large scale quantum computing systems. In this work, we develop an assembly language that makes it possible to easily map quantum circuits to the crossbar system, taking into account its planar architecture and control limitations. Using this assembly language we show how to implement well known quantum error correction codes such as the planar surface and color codes in this limited control setting with only a small overhead in time. Finally, using the quantum dot processor's ability to shuttle qubits around we develop a planar implementation of the 3D gauge color code, an error correction code that allows for universal fault tolerant quantum computing without the need for methods such as magic state distillation.

ABSTRACT. As opposed to the abstract Hilbert space formalism, the search for a more physical, or operational definition of quantum mechanics is an ongoing task. In the framework of no-signalling theories, one could try to find the set of physical principles that would allow exactly the set of quantum correlations. One of the such principles proposed is Macroscopic Locality (ML); it is shown to coincide with the first level of the Navascues-Pironio-Acin hierarchy (Q1) and known to be strictly larger than the quantum set. In this work, we propose a refinement of the principle of ML, called Many-box locality (MBL). Denote the a bipartite two-input two-output distribution p(ab|xy) (a box), where a,b=0,1. Imagine N such independent boxes, we define the N-box coarse-graining of p(ab|xy) to be the distribution of the sums of output, p(AB|xy), where A=sum_i a_i. A distribution belongs to MBL_N if its N-box coarse-graining is local. We characterized the MBL_N sets for small number of N for several slices of the no-signalling polytope. On some slices, we showed that MBL_inf coincides with Q1; while on another, there exists a super-quantum distribution that falls in MBL_inf.

ABSTRACT. Recently, a connection between quantum coherence and quantum steering was established and criteria for non-local advantage of quantum coherence were derived. Here, we derive a set of complementarity relations between the non-local advantages of quantum coherence achieved by various criteria.

ABSTRACT. We study local-realistic inequalities, Bell-type inequalities, for bipartite pure states of finite dimensional quantum systems -- qudits. There are a number of proposed Bell-type inequalities for such systems. Our interest is in relating the value of Bell-type inequality function with a measure of entanglement. Interestingly, we find that one of these inequalities, the Son-Lee-Kim inequality, can be used to measure entanglement of a pure bipartite qudit state and a class of mixed two-qudit states. Unlike the majority of earlier schemes in this direction, where number of observables needed to characterize the entanglement increases with the dimension of the subsystems, this method needs only four observables. We also discuss the experimental feasibility of this scheme. It turns out that current experimental set ups can be used to measure the entanglement using our scheme.

ABSTRACT. The time dynamics of quantum correlations in transverse anisotropic XY spin chain is studied at zero and finite temperatures. The evolution is due to the quenching of the couplings between the nearest-neighbor spins of the model, which is performed either within the same phase or across the quantum phase-transition point connecting the order-disorder phases of the model. We characterize the time-evolved entanglement and quantum discord, which exhibit varying behavior depending on the initial state and the quenching scheme. We show that the system is endowed with enhanced nearest-neighbor bipartite quantum correlations compared to that of the initial state, when quenched from the ordered to the deep disordered phase. However, nearest-neighbor quantum correlations are almost washed out when the system is quenched from the disordered to the ordered phase with the initial state being at the zero temperature. We find the condition for the occurrence of enhanced bipartite correlations when the system is quenched within the same phase. Moreover, we investigate the bipartite quantum correlations when the initial state is a thermal equilibrium state with finite temperature, which reveals the effects of thermal fluctuation on the phenomena observed at zero temperature.

ABSTRACT. The goal of entanglement distillation is to turn a large number of weakly entangled states into a smaller number of highly entangled ones. Practical entanglement distillation schemes offer a tradeoff between the fidelity to the target state, and the probability of succesful distillation. Exploiting such tradeoffs is of interest in the design of quantum repeater protocols. Here, we present a number of methods to assess and optimise entanglement distillation schemes. We start by giving a numerical method to compute upper bounds on the maximum achievable fidelity for a desired probability of success. This can be used to asses how well specific entangled states can be distilled in quantum network protocols. We show that this method performs well for many known examples by comparing it to well known distillation protocols. Indeed, we use it to prove optimality of the DEJMPS and EPL protocols for specific input states of interest. We proceed to present a method that can improve an existing distillation scheme for a given input state. An implementation of our numerical methods is available as an Julia package.

ABSTRACT. Quantum networks distributed over distances greater than a few kilometers will be limited by the time required for information to propagate between nodes. We analyze protocols that are able to circumvent this bottleneck by employing multi-qubit nodes and multiplexing. For each protocol, we investigate the key network parameters that determine its performance. We model achievable entangling rates based on the anticipated near-term performance of nitrogen-vacancy centres and other promising network platforms. This analysis allows us to compare the potential of the proposed multiplexed protocols in different regimes. Moreover, by identifying the gains that may be achieved by improving particular network parameters, our analysis suggests the most promising avenues for research and development of prototype quantum networks. Quantum Sci. Technol. 2 034002 (2017), doi:10.1088/2058-9565/aa7446

ABSTRACT. Why are cats never in a superposition of dead and alive? Usually, it is argued that decoherence makes sure that cats are never in a superposition: since the coherence time scales unfavourable with the size of the system, and because cats are relatively large, their coherence time is nihil. As quantum memory is scaled up, we are bound to encounter the same effects of the quantum-to-classical-transition.

One of the proposed solutions is to hide the quantum information in a subspace of the quantum register that is invulnerable to any noise. States in this subspace will not decohere, and therefore such a subspace is called a ‘Decoherence Free Subspace’ (DFS). These DFS’s were shown to be stable under first order perturbations of the noise, which means that if the noise differs slightly from what you expected it to be, the decoherence of states in the DFS is still negligible. However, we show that the second order effects still scale unfavourably with the number of qubits, which puts new limits on effectiveness with which DFS’s can be used to overcome decoherence.

ABSTRACT. The relentless attempts to contrive an all-comprehensive definition of randomness will always confront the complete bereft of mathematical reasoning that should meticulously delineate a conspicuous meaning of the word itself. However, solace could be found in the indecisiveness inherent to some dynamical physical processes, where the incorporation of noise within the mathematical framework of these processes will help us develop a similarity relationship among them all. On a practical level, the direct consequence of this established equivalency will be state preparation and environment engineering. Moreover, we will introduce a cheaper alternative to true random number generators. We believe that such analytical perspective will substantially embody the true identity of randomness.

ABSTRACT. We apply covert quantum communication based on entanglement generated from the Minkowski vacuum to the setting of quantum computation and quantum networks. Our approach hides the generation and distribution of entanglement in quantum networks by taking advantage of relativistic quantum effects. We devise a suite of covert quantum teleportation protocols that utilize the shared entanglement, local operations, and covert classical communication to transfer or process quantum information in stealth. As an application of our covert suite, we construct two prominent examples of measurement-based quantum computation, namely the teleportation-based quantum computer and the one-way quantum computer. In the latter case we explore the covert generation of graph states, and subsequently outline a protocol for the covert implementation of universal blind quantum computation.

ABSTRACT. We present a simple thermal machine in which two (d+1)-level quantum systems interact through resonant transitions, as well as through weak incoherent interactions with a hot and cold thermal bath respectively. The machine is autonomous, meaning that it has no source of external control or coherence. We show that one can probabilistically generate two maximally entangled d-level systems from the resulting steady state of the autonomous thermal machine.

ABSTRACT. Random local measurements have recently been proposed to construct entanglement witnesses and thereby detect the presence of bipartite entanglement. We experimentally demonstrate the efficacy of one such scheme on a two-qubit NMR quantum-information processor. We show that a set of three random local measurements suffices to detect the entanglement of a general two-qubit state. We experimentally generate states with different amounts of entanglement and show that the scheme is able to clearly witness entanglement. We perform complete quantum state tomography for each state and compute state fidelity to validate our results. Further, we extend previous results and perform a simulation using random local measurements to optimally detect bipartite entanglement in a hybrid system of 2⊗3 dimensionality.

ABSTRACT. For a variety of experiments, interferometers are an important tool. Frequently, the precise alignment of the two beams of the interferometers is one of the most time consuming parts of an optical experiment. We provide an easy alignment technique based on the weak value concept which requires only a single position sensitive detector to resolve deviations both in position and direction. For that purpose, we utilize the phase dependence of the average position of the interference pattern, which furthermore gets amplified with the weak value. Analyzing the position data over a 2 π phase scan yields the required correction parameters. With this method, the best overlap between the coherent components of both beams can be achieved with a single detector within a few experimental runs.

ABSTRACT. We construct a class of non-Markovian stochastic Schrödinger equations (SSE) driven by complex valued colored non-circular Gaussian noise. Instead of postulating the noise correlations, we show how the statistics of the noise process emerge from quantum measurements done on the the environment. We carefully discuss the Markov limit and obtain a SSE compatible with the Lindblad-Gorini-Kossakowski-Sudarshan quantum master equation. Lastly, we present an application to optimal entanglement detection in the presence of quantum memory effects.

ABSTRACT. In recent years multiple qubits have become the focus of research in quantum information, communication and metrology. These qubits provide the possibility of expanding the number of qubits without increasing the number of photons by increasing the number of modes per photon [1]. Orbital angular momentum (OAM) is a good candidate in this regard. Actually OAM modes included different value of ` construct a large orthonormal basis that can be used as a useful tool in a variety of applications such as high dimensional encoding [2], increasing the information capacity of an optical network, increasing the resolution and sensitivity of angular-displacement measurements performed by using an interferometer[3], and so on. For these applications of light carrying OAM, discriminating the photons with different OAM with a high separation efficiency is an important issue, which has attracted more attention in ongoing research. There are a lot of works in this regard, which they have been used different methods for discriminating different modes of OAM such as, employing fork diffraction gratings coupled into a single mode fiber [4], cascading of Mach-Zehnder interferometers with a Dove prism in each arm [5, 6], spiral phase plates, and q-plate technology [7, 8]. These methods has performed by using of bulky elements, which are not appropriate for measuring the OAM in integrated circuits. Here, we propose a scheme to determine which modes of the orbital angular momenta ` = 0, ±1 ~ , ±2 ~ light is carrying. Towards this aim, we should split the intended beam into two beams and by using an acousto-optic modulator (AOM) manipulate the frequency of one of the beams to a desired frequency. Then two beams go through a trapped atom and interact with that. We show by performing measurement on the internal state of the trapped atom one can determine the OAM of light however, without splitting or sorting the different modes. Actually we can only determine that light is included which one of the angular momenta ` = 0, ± ~ , and ±2 ~ only by tuning the frequency of the trap and beam. This schemes could find application in photonic integrated circuits. Moreover, due to the conservation of OAM, the OAM of the field is directly transferred to the atomic centre-of-mass motion (CM) of the atom. This would lead to an interesting result that just by tuning the frequency of the trap we could determine which mode of OAM can be transfered to the phonons of motional states of the atom.