SLOCC orbit of rank-deficient two-qubit states: quantum entanglement, quantum discord and EPR steering

Caban, Paweł; Rembieliński, Jakub; Smoliński, Kordian A.; Walczak, Zbigniew

doi:10.1007/s11128-017-1626-7

Cited by 6 publications

(3 citation statements)

References 30 publications

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“…Examples include steered coherence, [42][43][44] discord, [38,[45][46][47] entanglement [38,41,48] and EPR steering. [49][50][51][52][53][54] Zhang et al [55] experimentally verified the QSE of two-qubit states and also demonstrated volume monogamy relations of the QSE. [56] Recently, Du et al [57] investigated quantum phase transitions in the XXZ model through a QSE.…”

Section: Introductionmentioning

confidence: 95%

Visualizing and witnessing first-order coherence, Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame

Yang

Xing

Du³

et al. 2023

Chinese Phys. B

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Quantum steering ellipsoid (QSE) is a visual characterization for bipartite-qubit systems, and it is also a novel avenue for describing and detecting quantum correlations. Herein, by using the QSE, we visualize and witness the first-order coherence (FOC), the Bell nonlocality (BN), and the purity under the non-inertial frames. Also, the collective influences of the depolarizing channel and the non-coherence-generating channel (NCGC) on the FOC, the BN, and the purity are investigated in the QSE formalism. The results reveal that the distance from the center of QSE to the center of the Bloch sphere visualizes the FOC of bipartite system, the lengths of QSE semiaxis visualize the BN, and the QSE’s shape and position dominant the purity of system. One can capture the FOC, the BN, and the purity via the shape and position of the QSE in the non-inertial frames. The depolarizing channel (The NCGC) gives rise to the shrinking and degrading (the periodical oscillation) of the QSE. One can use these traits to visually characterize and detect the FOC, the BN, and the purity under the influences of external noises. Of particular note is that the condition for the QSE achieving the Bloch sphere’s center cannot be influenced by the depolarizing channel and the NCGC. The characteristics visualize that the conditions of the FOC disappearance are invariant under the additional influences of depolarizing channel and the NCGC, respectively.

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Section: Introductionmentioning

confidence: 95%

Visualizing and witnessing first-order coherence, Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame

Yang

Xing

Du³

et al. 2023

Chinese Phys. B

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“…In the case of two-partite, finite dimensional system being in the pure state, the Schmidt decomposition of the corresponding pure state gives essentially all relevant information on the corresponding quantum correlations. From the quantitative point of view and from qualitative ((S)LOCC type, semi-order relations [2,3,4,20,21] point of view as well. The case of many-partite systems, and also the case of mixed (even for two-partite systems) states is much less recognised despite to many efforts [2,3,4,5,22].…”

Section: Introductionmentioning

confidence: 99%

A Gramian Approach to Entanglement in Bipartite Finite Dimensional Systems: The case of pure states

Gielerak¹,

Sawerwain²

2019

Preprint

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It is observed that the reduced density matrices corresponding to pure states of bipartite qudits systems possess the Gram matrix structure. This observation has opened a possibility to analyse the entanglement in such systems from the purely geometrical point of view. In particular a new, of the geometrical nature quantitative measure of an entanglement has been proposed. Using the invented Gram matrix approach, a version of non-linear purification of a mixed states describing system analysed has been presented.

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“…Then, the necessary and sufficient conditions for an ellipsoid to represent a two-qubit state were proposed by Milne et al [22]. Many properties of two-qubit system can be captured by QSEs, such as entanglement [21][22][23], discord [21,24,25] and EPR steering [26][27][28][29][30][31]. Recently, Hu et al have explored the effect of a local trace-preserving single-qubit channel on a two-qubit state in the frame of QSEs and found that the quantum discord of a two-qubit state can be increased by local operations in QSE pictures [32].…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of maximal steered coherence and concurrence under decoherence

Yang¹,

Du²,

Sun³

et al. 2018

Laser Phys. Lett.

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In this work, by employing quantum steering ellipsoid (QSE) pictures, we investigate the dynamical characteristics of maximal steered coherence (MSC) and concurrence for an arbitrary Bell-diagonal state when the qubit-system suffers from canonical noisy channels, such as phase damping, bit flip and bit-phase flip channels. It has been found that the MSC is equal to the longest semiaxis length of the QSEs. Remarkably, the QSEs have an invariant semiaxis length under these mentioned unital channels. The dynamical behavior of MSC is dependent of the initial ellipsoid shape, and MSC is frozen to the length of invariant semiaxis ultimately. The time of frozen MSC can be derived by means of QSEs. Moreover, one can obtain that the concurrence depends on the sum of three semiaxis lengths of QSEs under these unital channels. Interestingly, the concurrence will be sudden death, if the sum of three semiaxis lengths is equal to 1. Additionally, we conclude that the time of entanglement sudden death can be deduced via QSE pictures.

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SLOCC orbit of rank-deficient two-qubit states: quantum entanglement, quantum discord and EPR steering

Cited by 6 publications

References 30 publications

Visualizing and witnessing first-order coherence, Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame

Visualizing and witnessing first-order coherence, Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame

A Gramian Approach to Entanglement in Bipartite Finite Dimensional Systems: The case of pure states

Dynamical behavior of maximal steered coherence and concurrence under decoherence

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