Bilocal classical theory: the independence of entanglement and complementarity

A standardly adopted notion of classicality is the following: a system is deemed classical if its set of states is a simplex. Also, it is traditionally excluded that a classical theory may admit of entangled states. This is of course the case for classical theory (CT). An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, will be presented. The theory, called bilocal classical theory (BCT), is endowed with a rule for composing an arbitrary number of systems, and with a nontrivial set of transformations. Moreover, BCT is proved to be well-posed using an exhaustive procedure to construct generic theories, along with a sufficient set of conditions to verify their consistency. Hence, BCT demonstrates that the presence of entanglement is independent of the existence of incompatible measurements. Some phenomena occurring in the theory are compatible with CT or quantum theory (QT)—such as the existence of a universal processor, cloning, entanglement swapping, dense coding, additivity of classical capacities—while others contradict both CT and QT, including: non-monogamous entanglement and hypersignaling. The theory is causal and satisfies the no-restriction hypothesis. At the same time, it violates a number of information-theoretic principles enjoyed by QT, most notably: local discriminability, purity of parallel composition of states, and purification. Some open problems raised by BCT will be pointed out. In particular, a no-go conjecture for the existence of a local-realistic ontological model associated with BCT will be formulated.

REFERENCES
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—Classicality without local discriminability: Decoupling entanglement and complementarity. Giacomo Mauro D’Ariano, Marco Erba, and Paolo Perinotti, Phys. Rev. A 102, 052216