Einstein–Podolsky–Rosen steering and the steering ellipsoid

Jevtic, Sania; Hall, Michael J. W.; Anderson, Malcolm; Zwierz, Marcin; Wiseman, Howard Mark

doi:10.1364/josab.32.000a40

Cited by 104 publications

(146 citation statements)

References 25 publications

(58 reference statements)

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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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“…Based on the concept of the steering ellipsoid [25], Ref. [23] derived a condition guaranteeing unsteerability of Bell diagonal two-qubit state. This method is however not applicable to general two-qubit states, for which unsteerability conditions are still missing.…”

Section: Introductionmentioning

confidence: 99%

Sufficient criterion for guaranteeing that a two-qubit state is unsteerable

et al. 2016

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Quantum steering can be detected via the violation of steering inequalities, which provide sufficient conditions for the steerability of quantum states. Here we discuss the converse problem, namely ensuring that an entangled state is unsteerable, and hence Bell local. We present a simple criterion, applicable to any two-qubit state, which guarantees that the state admits a local hidden state model for arbitrary projective measurements. Specifically, we construct local hidden state models for a large class of entangled states, which can thus not violate any steering or Bell inequality. In turn, this leads to sufficient conditions for a state to be only one-way steerable, and provides the simplest possible example of one-way steering. Finally, by exploiting the connection between steering and measurement incompatibility, we give a sufficient criterion for a continuous set of qubit measurements to be jointly measurable.

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“…In this work, we generalize the Barrett construction of an LHS model to a more general family of two-qubit states, those which can be considered as a mixture of Bell states, or Bell-diagonal states. Quantum steering of Belldiagonal states when measurements are limited to projective measurements has been recently understood [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Quantum steering of Bell-diagonal states with generalized measurements

Nguyen

Gühne

2020

Phys. Rev. A

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The phenomenon of quantum steering in bipartite quantum systems can be reduced to the question whether or not the first party can perform measurements such that the conditional states on the second party can be explained by a local hidden state model. Clearly, the answer to this depends on the measurements which the first party is able to perform. We introduce a local hidden state model explaining the conditional states for all generalized measurements on Bell-diagonal states of two qubits. More precisely, it is known for the restricted case of projective measurements and Bell-diagonal states characterised by the correlation matrix T that a local hidden state model exists if and only if RT = 2πNT |det(T )| ≥ 1, where NT is defined by an integral over the Bloch sphere. For generalized measurements described by positive operator valued measures we construct a model if RT ≥ 6/5. Our work paves the way for a systematic study of steerability of quantum states with generalized measurements beyond the highly-symmetric Werner states.

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Einstein–Podolsky–Rosen steering and the steering ellipsoid

Cited by 104 publications

References 25 publications

Superactivation of quantum steering

Superactivation of quantum steering

Sufficient criterion for guaranteeing that a two-qubit state is unsteerable

Quantum steering of Bell-diagonal states with generalized measurements

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