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arXiv:1603.05080 · Scientific Reports

EPR Steering inequalities with Communication Assistance

S. Nagy, Tamás Vértesi

Published Feb 16, 2016• 19 citations
arXivHTMLPDF

Abstract

In this paper, we investigate the communication cost of reproducing Einstein-Podolsky-Rosen (EPR) steering correlations arising from bipartite quantum systems. We characterize the set of bipartite quantum states which admits a local hidden state model augmented with c bits of classical communication from an untrusted party (Alice) to a trusted party (Bob). In case of one bit of information (c = 1), we show that this set has a nontrivial intersection with the sets admitting a local hidden state and a local hidden variables model for projective measurements. On the other hand, we find that an infinite amount of classical communication is required from an untrusted Alice to a trusted Bob to simulate the EPR steering correlations produced by a two-qubit maximally entangled state. It is conjectured that a state-of-the-art quantum experiment would be able to falsify two bits of communication this way.

DOI
10.1038/srep21634

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arXiv:1801.09891•Jan 30, 2018•1 citation
In this paper, we investigate the communication cost of reproducing Einstein-Podolsky-Rosen (EPR) steering correlations arising from bipartite quantum systems. We characterize the set of bipartite quantum states which admits a local hidden state model augmented with c bits of classical communication from an untrusted party (Alice) to a trusted party (Bob). In case of one bit of information (c = 1), we show that this set has a nontrivial intersection with the sets admitting a local hidden state and a local hidden variables model for projective measurements. On the other hand, we find that an infinite amount of classical communication is required from an untrusted Alice to a trusted Bob to simulate the EPR steering correlations produced by a two-qubit maximally entangled state. It is conjectured that a state-of-the-art quantum experiment would be able to falsify two bits of communication this way.
Einstein-Podolsky-Rosen (EPR) steering is an intermediate type of quantum nonlocality which sits between entanglement and Bell nonlocality. A set of correlations is Bell nonlocal if it does not admit a local hidden variable (LHV) model, while it is EPR nonlocal if it does not admit a local hidden variable--local hidden state (LHV-LHS) model. It is interesting to know what states can generate EPR-nonlocal correlations in the simplest nontrivial scenario, that is, two projective measurements for each party sharing a two-qubit state. Here we show that a two-qubit state can generate EPR-nonlocal full correlations (excluding marginal statistics) in this scenario if and only if it can generate Bell-nonlocal correlations. If full statistics (including marginal statistics) is taken into account, surprisingly, the same scenario can manifest the simplest one-way steering and the strongest hierarchy between steering and Bell nonlocality. To illustrate these intriguing phenomena in simple setups, several concrete examples are discussed in detail, which facilitates experimental demonstration. In the course of study, we introduce the concept of restricted LHS models and thereby derive a necessary and sufficient semidefinite-programming criterion to determine the steerability of any bipartite state under given measurements. Analytical criteria are further derived in several scenarios of strong theoretical and experimental interest.
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. EPR steering is a resource for quantum key distribution that is device independent on only one side in that it certifies bipartite entanglement when one party's device is not characterized while the other party's device is fully characterized. In this work, we introduce two types of genuine tripartite EPR steering, and derive two steering inequalities to detect them. In a semi-device-independent scenario where only the dimensions of two parties are assumed, the correlations which violate one of these inequalities also certify genuine tripartite entanglement. It is known that Alice can demonstrate bipartite EPR steering to Bob if and only if her measurement settings are incompatible. We demonstrate that quantum correlations can also detect tripartite EPR steering from Alice to Bob and Charlie, even if Charlie's measurement settings are compatible.
Monogamy inequalities for the way bipartite Einstein-Podolsky-Rosen (EPR) steering can be distributed among NNN systems are derived. One set of inequalities is based on witnesses with two measurement settings, and may be used to demonstrate correlation of outcomes between two parties, that cannot be shared with more parties. It is shown that the monogamy for steering is directional. Two parties cannot independently demonstrate steering of a third system, using the same two-setting steering witness, but it is possible for one party to steer two independent systems. This result explains the monogamy of two-setting Bell inequality violations and the sensitivity of the continuous variable (CV) EPR criterion to losses on the steering party. We generalize to mmm settings. A second type of monogamy relation gives the quantitative amount of sharing possible, when the number of parties is less than or equal to mmm, and takes a form similar to the Coffman-Kundu-Wootters relation for entanglement. The results enable characterization of the tripartite steering for CV Gaussian systems and qubit Greenberger-Horne-Zeilinger and WWW states.
Einstein-Podolsky-Rosen (EPR) steering, as a new form of nonlocality, stands between entanglement and Bell nonlocality, implying promising applications for quantum information tasks. The problem of detecting EPR steering plays an important role in characterization of quantum nonlocality. Despite some significant progress, one still faces a practical issue: how to detect EPR steering in an experimentally friendly fashion. Resorting to an EPR steering inequality, one is required to apply a strategy as efficiently as possible for any selected measurement settings on the two subsystems, one of which may not be trusted. Inspired by the recent powerful linear criteria proposed by Saunders et al. [D. J. Saunders, S. J. Jones, H. M. Wiseman, and G. J. Pryde, Nat. Phys. 6, 845 (2010).], we present an optimized method of certifying steering for an arbitrary-dimensional state in a cost-effective manner. We provide a practical way to signify steering via only a few settings to optimally violate the steering inequality. Our method leads to steering detections in a highly efficient way, and can be performed with any number of settings, for an arbitrary bipartite mixed state, which can reduce experimental overheads significantly.
Collective multipartite Einstein-Podolsky-Rosen (EPR) steering is a type of quantum correlation shared among N parties, where the EPR paradox of one party can only be realized by performing local measurements on all the remaining N-1 parties. We formalize the collective tripartite steering in terms of local hidden state model and give the steering inequalities that act as signatures and suggest how to optimize collective tripartite steering in specific optical schemes. The special entangled states with property of collective multipartite steering may have potential applications in ultra-secure multiuser communication networks where the issue of trust is critical.
Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are every important quantum correlations of a composite quantum system. Bell nonlocality of a bipartite state is a quantum correlation demonstrated by some local quantum measurements, while EPR steering is another form of quantum correlations, observed firstly by Schrodinger in the context of famous EPR paradox. In this paper, we give some remarks on Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity and closedness of the set of all Bell local states and the set of all EPR unsteerable states. We also derive a EPR-steering criteria, with which the EPR steerability of the maximally entangled states are checked.