Algorithmic Construction of Local Hidden Variable Models for Entangled Quantum States

Hirsch, Flavien; Quintino, Marco Túlio; Vértesi, Tamás; Pusey, Matthew F.; Brunner, Nicolás

doi:10.1103/physrevlett.117.190402

Cited by 72 publications

(133 citation statements)

References 35 publications

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“…This result implies that any two-qubit and any qubit-qutrit entangled state is k-copy steerable. Therefore, given previous results constructing LHS models for such entangled states [5,[27][28][29][30][31][32], we obtain many examples of super-activation of steering. Our results also allows us to put bounds on the minimal number of copies required for super-activation of steering and nonlocality.…”

Section: Introductionmentioning

confidence: 83%

“…First of all, the fact that every entangled 2 × 2 state is steerable for some number of copies k, together with the fact that there are numerous 2 × 2 entangled state admitting a LHS model [5,[27][28][29][30][31][32] is sufficient to show super-activation. The same is true of course for the case of 2 × 3 entangled states admitting a LHS model (from Alice to Bob).…”

Section: Super-activation Of Quantum Steeringmentioning

confidence: 99%

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Superactivation of quantum steering

2016

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We consider Einstein-Podolsky-Rosen steering in the regime where the parties can perform collective measurements on many copies of a given shared entangled state. We derive a simple and efficient condition for guaranteeing that an entangled state is k-copy steerable. In particular we show that any two-qubit and qubit-qutrit entangled states is k-copy steerable. This allows us to discuss the effect of super-activation of steering, whereby an entangled state that is unsteerable (i.e., admits a local hidden state model) in the one-copy regime becomes k-copy steerable. We provide examples with few copies and low dimensions. Our results give evidence that entanglement and steering could become equivalent in the multi-copy regime.

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Section: Introductionmentioning

confidence: 83%

Section: Super-activation Of Quantum Steeringmentioning

confidence: 99%

Superactivation of quantum steering

2016

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“…While this cannot be the case for all non-full-rank entangled states, as some of these admit a LHS model [26,27], it would be interesting to find examples of full-rank entangled states with infinite communication cost, or to prove that such states necessarily cannot exist.…”

Section: Discussionmentioning

confidence: 99%

Classical communication cost of quantum steering

et al. 2016

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Quantum steering is observed when performing appropriate local measurements on an entangled state. Here we discuss the possibility of simulating classically this effect, using classical communication instead of entanglement. We show that infinite communication is necessary for exactly simulating steering for any pure entangled state, as well as for a class of mixed entangled states. Moreover, we discuss the communication cost of steering for general entangled states, as well as approximate simulation. Our findings reveal striking differences between Bell nonlocality and steering, and provide a natural way of measuring the strength of the latter.Comment: 7 pages, 1 figure. See also arXiv:1603.xxxxx for related work by S. Nagy and T. V\'ertes

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“…Given that these sufficient conditions are likely to be suboptimal, an obvious question that follows is whether one can find an explicit threshold F thr that is smaller than that given by Theorem III.2 (Theorem B.1) such that F > F thr still guarantees steerability (Bell nonlocality). While this may seem like a difficult problem, recent advances [42] in the algorithmic construction of local hidden-variable (-state) models may shed some light on this. More generally, it will be interesting to know if our sufficient condition can be strengthened while preserving its computability.…”

Section: Discussionmentioning

confidence: 99%

Quantum steerability: Characterization, quantification, superactivation, and unbounded amplification

2016

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Quantum steering, also called Einstein-Podolsky-Rosen steering, is the intriguing phenomenon associated with the ability of spatially separated observers to steer-by means of local measurementsthe set of conditional quantum states accessible by a distant party. In the light of quantum information, all steerable quantum states are known to be resources for quantum information processing tasks. Here, via a quantity dubbed steering fraction, we derive a simple, but general criterion that allows one to identify quantum states that can exhibit quantum steering (without having to optimize over the measurements performed by each party), thus making an important step towards the characterization of steerable quantum states. The criterion, in turn, also provides upper bounds on the largest steering-inequality violation achievable by arbitrary finite-dimensional maximally entangled states. For the quantification of steerability, we prove that a strengthened version of the steering fraction is a convex steering monotone and demonstrate how it is related to two other steering monotones, namely, steerable weight and steering robustness. Using these tools, we further demonstrate the superactivation of steerability for a well-known family of entangled quantum states, i.e., we show how the steerability of certain entangled, but unsteerable quantum states can be recovered by allowing joint measurements on multiple copies of the same state. In particular, our approach allows one to explicitly construct a steering inequality to manifest this phenomenon. Finally, we prove that there exist examples of quantum states (including some which are unsteerable under projective measurements) whose steering-inequality violation can be arbitrarily amplified by allowing joint measurements on as little as three copies of the same state. For completeness, we also demonstrate how the largest steering-inequality violation can be used to bound the largest Bell-inequality violation and derive, analogously, a simple sufficient condition for Bell-nonlocality from the latter.

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Algorithmic Construction of Local Hidden Variable Models for Entangled Quantum States

Cited by 72 publications

References 35 publications

Superactivation of quantum steering

Superactivation of quantum steering

Classical communication cost of quantum steering

Quantum steerability: Characterization, quantification, superactivation, and unbounded amplification

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