{
  "id": "2008.04011",
  "version": "v1",
  "published": "2020-08-10T10:30:47.000Z",
  "updated": "2020-08-10T10:30:47.000Z",
  "title": "Classicality without local discriminability: decoupling entanglement and complementarity",
  "authors": [
    "Giacomo Mauro D'Ariano",
    "Marco Erba",
    "Paolo Perinotti"
  ],
  "comment": "24+7 pages, 2 figures, 1 table, plenty of diagrams",
  "categories": [
    "quant-ph"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-10T10:30:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local discriminability",
      "operational probabilistic theory",
      "decoupling entanglement",
      "construct generic operational probabilistic theories",
      "classicality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}