Correlation-based entanglement criteria for bipartite systems

Jing, Yumang; He, Qiongyi; Byrnes, Tim

doi:10.1103/physreva.95.052305

Cited by 3 publications

(2 citation statements)

References 38 publications

(43 reference statements)

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“…Especially, mathematical definitions of Bell nonlocality and EPR steerability of bipartite states were proposed and their characterizations were given in [17] by Cao and Guo. Although entanglement was first recognized as the characteristic trait of quantum mechanics [1], its role has been debated since it does not capture all the quantum features of a quantum system [32][33][34]. In the case of bipartite systems, the quantum discord (generally, quantum correlation) has been widely accepted as a fundamental tool due to its relevance in quantum computing tasks not relying on entanglement [32][33][34][35]. Luo in [36] established the mathematical definition of classical correlation and quantum correlation of a bipartite state by using measurement-induced disturbance to the state.…”

Section: Introductionmentioning

confidence: 99%

Some Measurement-Based Characterizations of Separability of Bipartite States

2021

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Importance of quantum entanglement has been demonstrated in various applications. Usually, separability of a bipartite state is defined by its algebraic structure, i.e. a convex combination of product states. But it seems to be hard to check separability (equivalently, entanglement) of a state from its algebraic structure. In this note, we give some characterizations of separability of bipartite states based on POVM measurements. For bipartite pure states, we prove the separability, Bell locality, unsteerability and classical correlation are the same. As a consequence, every entangled pure bipartite state is always Bell nonlocal, steerable and quantum correlated.

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Section: Introductionmentioning

confidence: 99%

Some Measurement-Based Characterizations of Separability of Bipartite States

2021

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“…from an experimental point of view) are simple criteria that can be evaluated based on a small number of observables. In this sense, criteria such as those given by Duan and co-workers [11], Hillery-Zubairy [12], entanglement witness [13][14][15][16], mutually unbiased bases [17], and others [18][19][20][21][22][23] are quite valuable as they can detect entanglement without full tomography of the density matrix.…”

Section: Introductionmentioning

confidence: 99%

Covariance matrix entanglement criterion for an arbitrary set of operators

Tripathi¹,

Radhakrishnan²,

Byrnes³

2018

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We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by performing a partial transposition on the operators. The method is highly efficient and versatile in the sense that the set of measurement operators can be freely chosen, do not need to be complete, and there is no constraint on the commutation relations. The method is particularly suited for systems with higher dimensionality since the computations do not scale with the dimension of the Hilbert space rather they scale with the number of chosen observables which can always be kept small. We illustrate the approach by examining the entanglement between two spin ensembles, and show that it detects entanglement in a basis independent way.

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Covariance matrix entanglement criterion for an arbitrary set of operators

2020

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A criterion for entanglement detection based on covariance matrices for an arbitrary set of observables is formulated. The method generalizes the covariance matrix entanglement criterion by Simon (2000 Phys. Rev. Lett. 84 2726) to a more general set of operators using the positive partial transpose test for the covariance matrix. The relation is found by starting from the generalized uncertainty relation for multiple operators, and taking the partial transpose on the bipartition. The method is highly efficient and versatile in the sense that the set of measurement operators can be freely chosen, and there is no constraint on the commutation relations. The main restriction on the chosen set of measurement operators is that the correlators and expectation values of the partially transposed observable operators can be evaluated. The method is particularly suited for systems with higher dimensionality since the computations do not scale with the dimension of the Hilbert space—rather they scale with the number of chosen observables. We illustrate the approach by examining the entanglement between two spin ensembles, and show that it detects entanglement in a basis independent way.

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Correlation-based entanglement criteria for bipartite systems

Cited by 3 publications

References 38 publications

Some Measurement-Based Characterizations of Separability of Bipartite States

Some Measurement-Based Characterizations of Separability of Bipartite States

Covariance matrix entanglement criterion for an arbitrary set of operators

Covariance matrix entanglement criterion for an arbitrary set of operators

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