Geometric steering criterion for two-qubit states

Yu, Bai-Chu; Jia, Zhih-Ahn; Wu, Yu-Chun; Guo, Guang‐Can

doi:10.1103/physreva.97.012130

Cited by 16 publications

(7 citation statements)

References 22 publications

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“…Necessary and sufficient conditions for steerability are in general not known. The exception is a two-qubit case, for which necessary and sufficient conditions are analysed in Nguyen and Vu [43] and Yu et al [61]. For other dimensions there are some partial results, for example, many inequalities providing sufficient conditions for steerability are derived in Calvacanti et al [8].…”

Section: Definition 34mentioning

confidence: 99%

Quantumness of States and Unitary Operations

Luc

2020

Found Phys

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This paper investigates various properties that may by possessed by quantum states, which are believed to be specifically “quantum” (entanglement, nonlocality, steerability, negative conditional entropy, non-zero quantum discord, non-zero quantum super discord and contextuality) and their opposites. It also considers their “absolute” counterparts in the following sense: a given state has a given property absolutely if after an arbitrary unitary transformation it still possesses it. The known relations between the listed properties and between their absolute counterparts are summarized. It is proven that the only two-qubit state that has zero quantum discord absolutely is the maximally mixed state. Finally, related conceptual issues concerning the terms “classical” and “quantum” are discussed.

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Section: Definition 34mentioning

confidence: 99%

Quantumness of States and Unitary Operations

Luc

2020

Found Phys

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“…Because of this fundamental and practical significance of EPR steering, it is interesting to develop tests for EPR steerability from Alice to Bob. Although general necessary and sufficient conditions for bipartite EPR steerability of quantum states are known [16,20,21], these criteria involve intricate optimization procedures. In those, even the simplest case of two qubits requires considerable numerical efforts to determine typical statistical features of bipartite EPR steerability, such as volume ratios of EPR steerable versus all quantum states [20].…”

Section: Introductionmentioning

confidence: 99%

Typical bipartite steerability and generalized local quantum measurements

Schumacher,

Alber

2023

Phys. Scr.

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Recently proposed correlation-matrix based sufficient conditions for bipartite steerability from Alice to Bob are applied to local informationally complete positive operator valued measures (POVMs) of the $(N,M)$-type. These POVMs allow for a unified description of a large class of local generalized measurements of current interest. It is shown that this sufficient condition exhibits a peculiar scaling property. It implies that all types of informationally complete $(N,M)$-POVMs are equally powerful in detecting bipartite steerability from Alice to Bob and, in addition, they are as powerful as local orthonormal hermitian operator bases (LOOs). In order to explore the typicality of steering numerical calculations of lower bounds on Euclidean volume ratios between steerable bipartite quantum states from Alice to Bob and all quantum states are determined with the help of a hit-and-run Monte-Carlo algorithm. These results demonstrate that with the single exception of two qubits this correlation-matrix based sufficient condition significantly underestimates these volume ratios. These results are also compared with a recently proposed method which reduces the determination of bipartite steerability from Alice's qubit to Bob's arbitrary dimensional quantum system to the determination of bipartite entanglement. It is demonstrated that in general this method is significantly more effective in detecting typical steerability provided entanglement detection methods are used which transcend local measurements.

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“…Later on, Costa et al proposed a measure of steering that is based on the maximal violation of the line steering inequality in the two-and three-measurement scenarios [4]. Recently, Guo et al [5] presented a steering criterion which is both necessary and sufficient for two-qubit states under arbitrary measurement sets. And a set of complementarity relations between steering or nonlocal advantage of quantum coherence inequalities can be derived and achieved by various criteria [6].…”

Section: Introductionmentioning

confidence: 99%

Constraint Relation Between Steerability and Concurrence for Two‐Qubit States

et al. 2021

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Entanglement and steering are used to describe quantum correlation. And steerable states form a strict subset of entangled states. A natural question arises concerning how much territory steerability occupies entanglement for a general two‐qubit entangled state. In this work, the constraint relation between steerability and concurrence is investigated by using two kinds of evolutionary states and any two‐qubit states (or lots of randomly generated states). By combining the theoretical and numerical proofs, the upper and lower boundaries of steerability are obtained. And the lower boundary can be used as a sufficient criterion for steering detection. Furthermore, a special kind of mixed state transformed by performing an arbitrary unitary transformation on Werner‐like state is considered, and a sufficient steering criterion described by concurrence and purity is proposed.

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Geometric steering criterion for two-qubit states

Cited by 16 publications

References 22 publications

Quantumness of States and Unitary Operations

Quantumness of States and Unitary Operations

Typical bipartite steerability and generalized local quantum measurements

Constraint Relation Between Steerability and Concurrence for Two‐Qubit States

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