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      Complementarity between signalling and local indeterminacy in quantum nonlocal correlations

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          Abstract

          The correlations that violate the CHSH inequality are known to have complementary contributions from signaling and local indeterminacy. This complementarity is shown to represent a strengthening of Bell's theorem, and can be used to certify randomness in a device-independent way, assuming neither the validity of quantum mechanics nor even no-signaling. We obtain general nonlocal resources that can simulate the statistics of the singlet state, encompassing existing results. We prove a conjecture due to Hall (2010) and Kar et al. (2011) on the complementarity for such resources.

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          Non-local correlations as an information theoretic resource

          Jonathan Barrett, Stefano Pironio, Serge Massar … (2004)
          It is well known that measurements performed on spatially separated entangled quantum systems can give rise to correlations that are non-local, in the sense that a Bell inequality is violated. They cannot, however, be used for super-luminal signalling. It is also known that it is possible to write down sets of ``super-quantum'' correlations that are more non-local than is allowed by quantum mechanics, yet are still non-signalling. Viewed as an information theoretic resource, super-quantum correlations are very powerful at reducing the amount of communication needed for distributed computational tasks. An intriguing question is why quantum mechanics does not allow these more powerful correlations. We aim to shed light on the range of quantum possibilities by placing them within a wider context. With this in mind, we investigate the set of correlations that are constrained only by the no-signalling principle. These correlations form a polytope, which contains the quantum correlations as a (proper) subset. We determine the vertices of the no-signalling polytope in the case that two observers each choose from two possible measurements with d outcomes. We then consider how interconversions between different sorts of correlations may be achieved. Finally, we consider some multipartite examples.
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            Maximally Non-Local and Monogamous Quantum Correlations

            Jonathan Barrett, Adrian Kent, Stefano Pironio (2006)
            We introduce a version of the chained Bell inequality for an arbitrary number of measurement outcomes, and use it to give a simple proof that the maximally entangled state of two d dimensional quantum systems has no local component. That is, if we write its quantum correlations as a mixture of local correlations and general (not necessarily quantum) correlations, the coefficient of the local correlations must be zero. This suggests an experimental programme to obtain as good an upper bound as possible on the fraction of local states, and provides a lower bound on the amount of classical communication needed to simulate a maximally entangled state in dxd dimensions. We also prove that the quantum correlations violating the inequality are monogamous among non-signalling correlations, and hence can be used for quantum key distribution secure against post-quantum (but non-signalling) eavesdroppers.
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              The Communication Cost of Simulating Bell Correlations

              B. Toner, D. Bacon (2003)
              What classical resources are required to simulate quantum correlations? For the simplest and most important case of local projective measurements on an entangled Bell pair state, we show that exact simulation is possible using local hidden variables augmented by just one bit of classical communication. Certain quantum teleportation experiments, which teleport a single qubit, therefore admit a local hidden variables model.
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                Author and article information

                Journal
                Publication date Created: 17 September 2013
                Publication date Updated: 2014-08-05
                Article
                ArXiV ID: 1309.4435
                SO-VID: f2bd158a-c001-4849-9d7f-a0bfeb266b4f
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Comments 5 pages, no figures; Accepted for publication in Quantum Information and Computation
                Categories quant-ph

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