Download PDFOpen PDF in browser“Two bits less” after quantuminformation conservation and their interpretation as “distinguishability / indistinguishability” and “classical / quantum”EasyChair Preprint no. 59527 pages•Date: June 29, 2021AbstractThe paper investigates the understanding of quantum indistinguishability after quantum information in comparison with the “classical” quantum mechanics based on the separable complex Hilbert space. The two oppositions, correspondingly “distinguishability / indistinguishability” and “classical / quantum”, available implicitly in the concept of quantum indistinguishability can be interpreted as two “missing” bits of classical information, which are to be added after teleportation of quantum information to be restored the initial state unambiguously. That new understanding of quantum indistinguishability is linked to the distinction of classical (MaxwellBoltzmann) versus quantum (either FermiDirac or BoseEinstein) statistics. The latter can be generalized to classes of wave functions (“empty” qubits) and represented exhaustively in Hilbert arithmetic therefore connectible to the foundations of mathematics, more precisely, to the interrelations of propositional logic and set theory sharing the structure of Boolean algebra and two antiisometric copies of Peano arithmetic. Keyphrases: BoseEinstein Statistics, FermiDirac Statistics, Hilbert arithmetic, MaxwellBoltzmann statistics, quantum indistinguishability, quantuminformation conservation, qubit Hilbert space, teleportation
