All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering

Chen, Jing-Ling; Ye, Xiang-Jun; Wu, Chunfeng; Su, Hong-Yi; Cabello, Adán; Kwek, L. C.; Oh, C. H.

doi:10.1038/srep02143

Cited by 76 publications

(76 citation statements)

References 25 publications

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“…Recently, an inequality to delineate quantum steering from other non-local properties was proposed [4][5][6] and tested in a range of experiments [6,7]. Steerability has since then been further investigated with all-versus-nothing measures [8], and has been utilized as a way to characterize and visualize the state-space of two-qubit systems [9]. In combination these different concepts (Bell non-locality, steerability, and entanglement) form a hierarchy and enable one to categorize different non-local properties of quantum states.…”

Section: Introductionmentioning

confidence: 99%

Temporal steering inequality

et al. 2014

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Quantum steering is the ability to remotely prepare different quantum states by using entangled pairs as a resource. Very recently, the concept of steering has been quantified with the use of inequalities, leading to substantial applications in quantum information and communication science. Here, we highlight that there exists a natural temporal analogue of the steering inequality when considering measurements on a single object at different times. We give non-trivial operational meaning to violations of this temporal inequality by showing that it is connected to the security bound in the BB84 protocol and thus may have applications in quantum communication.

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Section: Introductionmentioning

confidence: 99%

Temporal steering inequality

et al. 2014

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“…Until now, the fundamental theorem has achieved ubiquitous applications in different quantum information tasks, such as quantum key distribution [5], communication complexity [6], and random number generation [7].Unlike quantum entanglement and Bell's nonlocality, the research field of quantum steering has been sterile till 2007, when Wiseman, Jones, and Doherty [8] reformulated the idea and placed it firmly on a rigorous ground. Since then EPR steering has gained a very rapid development in both theories [9][10][11][12][13][14][15]17] and experiments [18][19][20][21][22][23][24][25][26][27].…”

mentioning

confidence: 99%

Bell’s Nonlocality Can be Detected by the Violation of Einstein-Podolsky-Rosen Steering Inequality

Chen¹,

Ren²,

Chen³

et al. 2016

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Recently quantum nonlocality has been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell’s nonlocality. Among which, Bell’s nonlocality is the strongest type. Bell’s nonlocality for quantum states is usually detected by violation of some Bell’s inequalities, such as Clause-Horne-Shimony-Holt inequality for two qubits. Steering is a manifestation of nonlocality intermediate between entanglement and Bell’s nonlocality. This peculiar feature has led to a curious quantum phenomenon, the one-way Einstein-Podolsky-Rosen steering. The one-way steering was an important open question presented in 2007, and positively answered in 2014 by Bowles et al., who presented a simple class of one-way steerable states in a two-qubit system with at least thirteen projective measurements. The inspiring result for the first time theoretically confirms quantum nonlocality can be fundamentally asymmetric. Here, we propose another curious quantum phenomenon: Bell nonlocal states can be constructed from some steerable states. This novel finding not only offers a distinctive way to study Bell’s nonlocality without Bell’s inequality but with steering inequality, but also may avoid locality loophole in Bell’s tests and make Bell’s nonlocality easier for demonstration. Furthermore, a nine-setting steering inequality has also been presented for developing more efficient one-way steering and detecting some Bell nonlocal states.

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“…Recently, it has been demonstrated that violation of a steering inequality is necessary for one-sided device-independent quantum key distribution [16]. EPR steering admits an asymmetric formulation: there exist entangled states which are one-way steerable, i.e., demonstrate steerability from one observer to the other observer but not vice-versa [17,18]. Various other steering criteria have also been proposed such as all versus nothing proof of EPR steering [17] and hierarchy of steering criteria based on moments [19].…”

Section: Introductionmentioning

confidence: 99%

“…EPR steering admits an asymmetric formulation: there exist entangled states which are one-way steerable, i.e., demonstrate steerability from one observer to the other observer but not vice-versa [17,18]. Various other steering criteria have also been proposed such as all versus nothing proof of EPR steering [17] and hierarchy of steering criteria based on moments [19]. Motivated by the question of how much a steering scenario demonstrates steerability, a measure of steering called steering weight was defined in Ref.…”

Section: Introductionmentioning

confidence: 99%

Cost of Einstein-Podolsky-Rosen steering in the context of extremal boxes

et al. 2018

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Einstein-Podolsky-Rosen steering is a form of quantum nonlocality which is weaker than Bell nonlocality, but stronger than entanglement. Here we present a method to check Einstein-Podolsky-Rosen steering in the scenario where the steering party performs two black-box measurements and the trusted party performs projective qubit measurements corresponding to two arbitrary mutually unbiased bases. This method is based on decomposing the measurement correlations in terms of extremal boxes of the steering scenario. In this context, we propose a measure of steerability called steering cost. We show that our steering cost is a convex steering monotone. We illustrate our method to check steerability with two families of measurement correlations and find out their steering cost.

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All-Versus-Nothing Proof of Einstein-Podolsky-Rosen Steering

Cited by 76 publications

References 25 publications

Temporal steering inequality

Temporal steering inequality

Bell’s Nonlocality Can be Detected by the Violation of Einstein-Podolsky-Rosen Steering Inequality

Cost of Einstein-Podolsky-Rosen steering in the context of extremal boxes

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