Quantum steerability based on joint measurability

Chen, Zhihua; Ye, Xiang-Jun; Fei, Shao-Ming

doi:10.1038/s41598-017-15910-8

Cited by 5 publications

(4 citation statements)

References 45 publications

(59 reference statements)

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“…Such transformations can be represented by matrix multiplication in homogeneous coordinates, by a 3 × 3 invertible matrix H. That is, the projective point⃗ x is transformed to H⃗ x. If we begin with the conic in equation (33), after the transformation these points satisfy (H −1 ⃗ x) ⊤ A(H −1 ⃗ x) = 0. This means that the matrix defining the conic transforms as…”

Section: Projective Geometrymentioning

confidence: 99%

On the power of one pure steered state for EPR-steering with a pair of qubits

2023

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As originally introduced, the EPR phenomenon was the ability of one party (Alice) to steer, by her choice between two measurement settings, the quantum system of another party (Bob) into two distinct ensembles of pure states. As later formalized as a quantum information task, EPR-steering can be shown even when the distinct ensembles comprise mixed states, provided they are pure enough and different enough. Consider the scenario where Alice and Bob each have a qubit and Alice performs dichotomic projective measurements. In this case, the states in the ensembles to which she can steer form the surface of an ellipsoid ${\cal E}$ in Bob's Bloch ball. Further, let the steering ellipsoid ${\cal E}$ have nonzero volume. It has previously been shown that if Alice's first measurement setting yields an ensemble comprising {\em two} pure states, then this, plus any one other measurement setting, will demonstrate EPR-steering. Here we consider what one can say if the ensemble from Alice's first setting contains only {\em one} pure state $\mathsf{p}\in{\cal E}$, occurring with probability $p_\mathsf{p}$. Using projective geometry, we derive the necessary and sufficient condition analytically for Alice to be able to demonstrate EPR-steering of Bob's state using this and some second setting, when the two ensembles from these lie in a given plane. Based on this, we show that, for a given ${\cal E}$, if $p_\mathsf{p}$ is high enough [$p_{\sf p} > p_{\rm max}^{{\cal E}} \in [0,1)$] then {\em any} distinct second setting by Alice is sufficient to demonstrate EPR-steering. Similarly we derive a $p_{\rm min}^{{\cal E}}$ such that $p_\mathsf{p}>p_{\rm min}^{{\cal E}}$ is necessary for Alice to demonstrate EPR-steering using only the first setting and {\em some} other setting. Moreover, the expressions we derive are tight; for spherical steering ellipsoids, the bounds coincide: $p_{\rm max}^{{\cal E}} = p_{\rm min}^{{\cal E}}$.

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Section: Projective Geometrymentioning

confidence: 99%

On the power of one pure steered state for EPR-steering with a pair of qubits

2023

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“…The definition of steering through informational properties, allows its analysis in theories involving quantum operators and quantum protocols, for instance by way of POVMs [96,185]. Even more, steering was proved completely equivalent to the capacity to carry out joint generalized measurements [186][187][188][189][190][191]; this means that the measurements that cannot be realized at the same time are the ones that reveal steering.…”

Section: Information Theorymentioning

confidence: 99%

“…In [189] a steering measure is found for the case of two-qubit, two-settings, from the correspondence of steering with joint measurability. In the sense of the distance to the unsteerable assemblages (see section 3.2.3.2), a class of steerable states is defined, for which upper and lower bounds are found that are related to the nonlocality given by maximal violation of the CHSH inequality.…”

Section: Other Informational Measuresmentioning

confidence: 99%

Certification and applications of quantum nonlocal correlations

Piceno-Martínez,

Rosales-Zárate,

Ornelas-Cruces

2023

J. Phys. Photonics

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Entanglement and Einstein-Podolsky-Rosen (EPR) steering are nonlocal quantum correlations, which are relevant resources for quantum information protocols. EPR steering, or quantum steering, refers to the correlation where a party might “steer”, or modify, the state of another, which is spatially separated. Entanglement is a symmetric resource while steering is asymmetrical, since it depends on the direction of the effect. Due to these different characteristics and the therefore different possible applications, there has been both theoretical and experimental research on forms to certify the distinct quantum nonlocal correlations. In recent years, alongside the investigation on quantum correlations between two systems, there has been a great interest in investigating multipartite/multimode entanglement as well as steering, since they include a high dimension and it may be possible to store more information than in a single qubit. In this review, we will summarize the different criteria and measures that have been developed for the characterization of these two kinds of correlations. We first focus on bipartite entanglement and steering. We then review the progress that has been made in the investigation of multipartite quantum correlations. We revise the theoretical work in quantum nonlocal correlation witnesses and measures, which respectively allow one to certify that the system is entangled or presents EPR steering, and give a quantification of the content of these correlations in the system. Then, we briefly review the experiments that have been designed and that demonstrate multipartite quantum correlations. We also include applications in quantum information protocols, in particular in quantum teleportation and quantum cryptography.

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“…It should be noted that this steering criterion can be also derived from the result of Ref. [52]. However, our criteria from Theorem 1 and 2 do not need to know the detailed state.…”

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confidence: 95%

Detecting EPR steering via two classes of local measurements

Lai¹,

Li²,

Fei³

et al. 2020

Quantum Inf Process

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We study the Einstein-Podolsky-Rosen (EPR) steering and present steerability criteria for arbitrary qubit-qudit (qudit-qubit) systems based on mutually unbiased measurements (MUMs) and general symmetric informationally complete measurements (general SIC-POVMs). Avoiding the usual complicated steering inequalities, these criteria can be more operational than some existing criteria and implemented experimentally. Detailed examples are given to illustrate the efficiency of the criteria in both computation and experimental implementation. *

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Quantum steerability based on joint measurability

Cited by 5 publications

References 45 publications

On the power of one pure steered state for EPR-steering with a pair of qubits

On the power of one pure steered state for EPR-steering with a pair of qubits

Certification and applications of quantum nonlocal correlations

Detecting EPR steering via two classes of local measurements

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