Number of spin<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>I</mml:mi></mml:mrow></mml:math>states for bosons

Zhang, L. H.; Zhao, Y. M.; Jia, Lu

doi:10.1103/physrevc.77.014301

Cited by 42 publications

(70 citation statements)

References 9 publications

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“…Therefore, we should not assess one as either stronger or weaker than the other criterion, but rather complementing each other. There are also nonlinear extensions of the CCNR criterion using, for instance, the local uncertainty relations or covariance matrices [10][11][12][13], and other feasible methods [14]. Nevertheless, here we will not consider such extensions.…”

Section: Introductionmentioning

confidence: 99%

Enhanced entanglement criterion via symmetric informationally complete measurements

et al. 2018

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We show that a special type of measurements, called symmetric informationally complete positive operator-valued measures (SIC POVMs), provide a stronger entanglement detection criterion than the computable cross-norm or realignment criterion based on local orthogonal observables. As an illustration, we demonstrate the enhanced entanglement detection power in simple systems of qubit and qutrit pairs. This observation highlights the significance of SIC POVMs for entanglement detection.

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Section: Introductionmentioning

confidence: 99%

Enhanced entanglement criterion via symmetric informationally complete measurements

et al. 2018

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“…Similarly to (7), we denote r = (r 0,1 , · · · , r 0,d1−1 , · · · , r d1−1,0 , · · · , r d1−1,d1−1 ) t and s = (s 0,1 , · · · , s 0,d2−1 , · · · , s d2−1,0 , · · · , s d2−1,d2−1 ) t , where t stands for transpose. Set T = (t ij ), where the entries t ij are given by the coefficients t lmkn , l, m = 0, · · · , d 1 − 1, k, n = 0, · · · , d 2 − 1, (l, m), (k, n) = (0, 0), with the first two indices lm associated with the array index i, and the last two indices kn with the column index j of T .…”

Section: Separability Criteria For Bipartite Statesmentioning

confidence: 99%

“…One basic problem is to determine whether a given bipartite state is entangled or separable. Although the problem is believed to be a nondeterministic polynomial-time hard problem, there are a number of operational criteria to deal with the problem, for example, the positive partial transpose (PPT) criterion [2,3], realignment criteria [4][5][6][7][8], covariance matrix criteria [9][10][11], correlation matrix criteria [12][13][14] and so on. More recently, some more separability criteria have been proposed [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Separability criteria based on Heisenberg–Weyl representation of density matrices

Chang¹,

Cui²,

Zhang

et al. 2018

Chinese Phys. B

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Separability is an important problem in theory of quantum entanglement. By using the Bloch representation of quantum states in terms of the Heisenberg-Weyl observable basis, we present a new separability criterion for bipartite quantum systems. It is shown that this criterion can be better than the previous ones in detecting entanglement. The results are generalized to multipartite quantum states.

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“…Then, for separable states, the bound (Hofmann and Takeuchi, 2003). This is a very strong entanglement criterion and its properties have been studied in detail (Gittsovich et al, 2008;Gühne et al, 2006;Zhang et al, 2008).…”

Section: Steering Criteria Based On Local Uncertainty Relationsmentioning

confidence: 99%

Quantum steering

et al. 2020

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Quantum correlations between two parties are essential for the argument of Einstein, Podolsky, and Rosen in favour of the incompleteness of quantum mechanics. Schrödinger noted that an essential point is the fact that one party can influence the wave function of the other party by performing suitable measurements. He called this phenomenon quantum steering and studied its properties, but only in the last years this kind of quantum correlation attracted significant interest in quantum information theory. In this paper we review the theory of quantum steering. We first present the basic concepts of steering and local hidden state models and their relation to entanglement and Bell nonlocality. Then, we describe the various criteria to characterize steerability and structural results on the phenomenon. A detailed discussion is given on the connections between steering and incompatibility of quantum measurements. Finally, we review applications of steering in quantum information processing and further related topics. 34 J. Quantum teleportation 34 K. Resource theory of steering 35 L. Post-quantum steering 36 M. Historical aspects of steering 36 1. Discussions between Schrödinger and Einstein 36 2. The two papers by Schrödinger 37 3. Impact of these papers 38 VI. Conclusion 38 References 39 arXiv:1903.06663v2 [quant-ph]

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Number of spinIstates for bosons

Cited by 42 publications

References 9 publications

Enhanced entanglement criterion via symmetric informationally complete measurements

Enhanced entanglement criterion via symmetric informationally complete measurements

Separability criteria based on Heisenberg–Weyl representation of density matrices

Quantum steering

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