This paper studies the so-called generalized multiplicative connectives of linear logic, focusing on the question of finding the ``non-decomposable'' ones, i.e., those that may not be expressed as combinations of the default binary connectives of multiplicative linear logic, Tensor and Par. In particular, we concentrate on generalized connectives of a surprisingly simple form, called ``entangled connectives'', and prove a characterization theorem giving a criterion for identifying the decomposable (resp., undecomposable) entangled connectives.