Classicality without local discriminability: decoupling entanglement and complementarity

• URL: http://arxiv.org/abs/2008.04011v6
• Date: Fri, 21 Jan 2022 16:30:10 GMT
• Title: Classicality without local discriminability: decoupling entanglement and complementarity
• Authors: Giacomo Mauro D'Ariano, Marco Erba, Paolo Perinotti
• Abstract summary: An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. We demonstrate that the presence of entanglement is independent of the existence of incompatible measurements. We also prove the existence, in the theory, of a universal processor.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a nontrivial set of transformations. Hence, we demonstrate that the presence of entanglement is independent of the existence of incompatible measurements. We then study a variety of phenomena occurring in the theory -- some of them contradicting both Classical and Quantum Theories -- including: cloning, entanglement swapping, dense coding, additivity of classical capacities, non-monogamous entanglement, hypersignaling. We also prove the existence, in the theory, of a universal processor. The theory is causal and satisfies the no-restriction hypothesis. At the same time, it violates a number of information-theoretic principles enjoyed by Quantum Theory, most notably: local discriminability, purity of parallel composition of states, and purification. Moreover, we introduce an exhaustive procedure to construct generic operational probabilistic theories, and a sufficient set of conditions to verify their consistency. In addition, we prove a characterisation theorem for the parallel composition rules of arbitrary theories, and specialise it to the case of bilocal-tomographic theories. We conclude pointing out some open problems. In particular, on the basis of the fact that every separable state of the theory is a statistical mixture of entangled states, we formulate a no-go conjecture for the existence of a local-realistic ontological model.

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