Quantum Steering and Spacelike Separation

Navascués, Miguel; Pérez-Garcı́a, David

doi:10.1103/physrevlett.109.160405

Cited by 15 publications

(12 citation statements)

References 29 publications

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“…Several * These two authors contributed equally to this work. theoretical [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and experimental studies [23][24][25][26][27][28][29][30][31] have focused on the verification and applications of EPR steering. Experimental demonstrations of one-way steering with the measurements restricted to Gaussian measurements have been reported [24,25].…”

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confidence: 99%

Experimental Quantification of Asymmetric Einstein-Podolsky-Rosen Steering

et al. 2016

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Einstein-Podolsky-Rosen (EPR) steering describes the ability of one observer to nonlocally "steer" the other observer's state through local measurements. EPR steering exhibits a unique asymmetric property, i.e., the steerability can differ between observers, which can lead to one-way EPR steering in which only one observer obtains steerability in the steering process. This property is inherently different from the symmetric concepts of entanglement and Bell nonlocality, and it has attracted increasing interest. Here, we experimentally demonstrate asymmetric EPR steering for a class of two-qubit states in the case of two measurement settings. We propose a practical method to quantify the steerability. We then provide a necessary and sufficient condition for EPR steering and clearly demonstrate one-way EPR steering. Our work provides new insight into the fundamental asymmetry of quantum nonlocality and has potential applications in asymmetric quantum information processing.Quantum nonlocality, which does not have a counterpart in classical physics, is the characteristic feature of quantum mechanics. First noted in the famous paper published by Einstein, Podolsky and Rosen (EPR) in 1935 [1], which aimed to argue the completeness of quantum mechanics, the content of quantum nonlocality has been greatly extended. In 2007, Wiseman et al. summarized the different conditions of quantum nonlocality and reformulated the concept of steering [2] originally introduced by Schrödinger [3] in response to the EPR paper (usually referred to as EPR steering), which stands between entanglement [1] and Bell nonlocality [4] in the hierarchy. In the view of a quantum information task, EPR steering can be regarded as the distribution of entanglement from an untrusted party, whereas entangled states need both parties to trust each other, and Bell nonlocality is presented on the premise that they distrust each other [5,6]. As a result, some entangled states cannot be employed to realize steering, and some steerable states do not violate Bell-like inequalities. EPR steering provides a novel insight into quantum nonlocality, and it exhibits an inherent asymmetric feature that differs from both entanglement and Bell nonlocality. Consider two observers, Alice and Bob, who share entangled states. There are cases in which the ability of Alice to steer Bob's state is not equal to the ability of Bob to steer Alice's state. There are also situations in which Alice can steer Bob's state but Bob cannot steer Alice's state, or vice versa; these situations are referred to as one-way steering [2,7]. Several * These two authors contributed equally to this work. theoretical [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and experimental studies [23][24][25][26][27][28][29][30][31] have focused on the verification and applications of EPR steering. Experimental demonstrations of one-way steering with the measurements restricted to Gaussian measurements have been reported [24,25]. A class of entangled qubit states that can be used to show th...

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confidence: 99%

Experimental Quantification of Asymmetric Einstein-Podolsky-Rosen Steering

et al. 2016

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“…Here we note that for the free case, we should also care about the quantum values of steering inequalities. Due to M. Navascués and D. Pérez-García's work, there are two different ways to define them [21]. One is in a commuting way that means the system described by a total Hilbert space, and the other one is the total system described in a tensor form.…”

Section: N Are Chosen To Be Free Observables Then the Local Hidden St...mentioning

confidence: 99%

Random and free observables saturate the Tsirelson bound for CHSH inequality

Yin,

Harrow,

Horodecki

et al. 2015

Preprint

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Maximal violation of the CHSH-Bell inequality is usually said to be a feature of anticommuting observables. In this work we show that even random observables exhibit near-maximal violations of the CHSH-Bell inequality. To do this, we use the tools of free probability theory to analyze the commutators of large random matrices. Along the way, we introduce the notion of "free observables" which can be thought of as infinite-dimensional operators that reproduce the statistics of random matrices as their dimension tends towards infinity. We also study the fine-grained uncertainty of a sequence of free or random observables, and use this to construct a steering inequality with a large violation.

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“…In infinite dimensions, S 2 = S 1 in general, so it can happen that repeated independent random measurements do not thermalize, i.e., that the map lim N →∞ Ω N is well defined in S 2 ∼ = H ⊗ H but nevertheless the sequence of states lim N →∞ Ω N (ρ) does not converge to any quantum state (any element of S 1 ). Such a non-trivial phenomenon is called Heat Vision [11], and, under some fair assumptions on the structure of the hamiltonian operator of the system 1 , is always accompanied by an unbounded energy increase. As shown in [11], the Heat Vision effect can be observed even in infinite dimensional systems with just two von Neumann measurements of two outcomes each.…”

Section: Theorem 5 Tsirelson's Theoremmentioning

confidence: 99%

“…Such a non-trivial phenomenon is called Heat Vision [11], and, under some fair assumptions on the structure of the hamiltonian operator of the system 1 , is always accompanied by an unbounded energy increase. As shown in [11], the Heat Vision effect can be observed even in infinite dimensional systems with just two von Neumann measurements of two outcomes each. Tsirelson's theorem can therefore be extended in the following way:…”

Section: Theorem 5 Tsirelson's Theoremmentioning

confidence: 99%

A Physical Approach to Tsirelson’s Problem

Navascues¹,

Cooney²,

Pérez-Garcı́a³

et al. 2012

Found Phys

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Tsirelson's problem deals with how to model separate measurements in quantum mechanics. In addition to its theoretical importance, the resolution of Tsirelson's problem could have great consequences for device independent quantum key distribution and certified randomness. Unfortunately, understanding present literature on the subject requires a heavy mathematical background. In this paper, we introduce quansality, a new theoretical concept that allows to reinterpret Tsirelson's problem from a foundational point of view. Using quansality as a guide, we recover all known results on Tsirelson's problem in a clear and intuitive way.

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Quantum Steering and Spacelike Separation

Cited by 15 publications

References 29 publications

Experimental Quantification of Asymmetric Einstein-Podolsky-Rosen Steering

Experimental Quantification of Asymmetric Einstein-Podolsky-Rosen Steering

Random and free observables saturate the Tsirelson bound for CHSH inequality

A Physical Approach to Tsirelson’s Problem

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