Estimating quantum steering and Bell nonlocality through quantum entanglement in two-photon systems

Yang, Huan; Zhao, Fa; Fan, Xiao-Gang; Ding, Zhiyong; Wang, Dong; Song, Xue-Ke; Yuan, Hao; Zhang, Changjin; Liu, Ye

doi:10.1364/oe.430964

Cited by 8 publications

(9 citation statements)

References 47 publications

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“…The Costa-Angelo measure S 3 of steering in the 3MS is sometimes modified as (see, e.g., Refs. [35,40]):…”

Section: Quantum Steering Measuresmentioning

confidence: 99%

“…The CHSH inequality in (20) is satisfied iff M (σ) ≤ 1. For a better comparison with other measures of quantum correlations defined in the range [0,1], the Bell nonlocality measure of Horodecki et al [57] can be given by (see, e.g., [40,47,62])…”

Section: Bell Nonlocality Measuresmentioning

confidence: 99%

“…Experimental QST-based hierarchies of quantum entanglement, steering, and Bell nonlocality for specific classes of twoqubit states in relation to the above-mentioned estimations were also reported. These include experiments with mixtures of partially entangled two-qubit pure states [40] and GWSs based on full QST [9] or full quantum process tomography [24]. A hierarchy of the latter states is also experimentally studied here but without applying a full QST.…”

Section: Introductionmentioning

confidence: 99%

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Experimental hierarchy of two-qubit quantum correlations without state tomography

Abo¹,

Soubusta²,

Jiráková³

et al. 2023

Preprint

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A Werner state, which is the singlet Bell state affected by white noise, is a prototype example of states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality by controlling the amount of noise. However, experimental demonstrations of this hierarchy in a sufficient and necessary way (i.e., by applying measures or universal witnesses of these quantum correlations) required so far full quantum state tomography, which is based on measuring at least 15 real parameters of two-qubit states. Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of twoqubit Stokes parameters. We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise.

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“…The Costa-Angelo measure S 3 of steering in the 3MS is sometimes modified as (see, e.g., Refs. [35,40]):…”

Section: Quantum Steering Measuresmentioning

confidence: 99%

Section: Bell Nonlocality Measuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Experimental hierarchy of two-qubit quantum correlations without state tomography

Abo¹,

Soubusta²,

Jiráková³

et al. 2023

Preprint

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show abstract

“…One can detect the BN of a system by violating some Bell-type inequalities, [22][23][24][25][26][27][28][29][30][31][32] especially the Clauser-Horne-Shimony-Holt (CHSH) inequality. [30][31][32][33][34] It deserves to be emphasized that not all entangled states can possess BN. [35] Horodecki et al have derived the sufficient and necessary conditions for BN for arbitrary bipartite states.…”

Section: Introductionmentioning

confidence: 99%

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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“…Beyond these steering criteria, several inequalities in terms of the sufficient conditions of steerability are used to detect steerability [11][12][13][14][15][16][17][18][19][20][21][22]. The experiments on the detection of EPR steering have also been reported [23][24][25][26][27][28][29][30][31]. With the steering criteria and sufficient conditions of steerability, the trade-off relation [32,33] and the hierarchy relation [34] between EPR steering and other quantum correlations have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Relating EPR steering with the fidelity of quantum teleportation for two- and three-qubit states

Fan

Qiu

Jia

et al. 2023

J. Phys. A: Math. Theor.

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EPR steering is an important quantum resource in quantum information and computation. The relationships between EPR steering and the fidelity of quantum teleportation for two- and three-qubit states are investigated in this paper. For two-qubit states, the upper bound of the average teleportation fidelity based on the EPR steering is derived. When the receiver can only perform the identity or the Pauli rotation operations, the two-qubit X-type states which violate the three-setting measurements steering inequality could be used for teleportation. In the end, the steering observables and the average teleportation fidelities of two-qubit reduced states for three-qubit pure states maintain the same ordering. The complementary relations between the steerable observables and the average teleportation fidelities for three-qubit pure states are also established.

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Estimating quantum steering and Bell nonlocality through quantum entanglement in two-photon systems

Cited by 8 publications

References 47 publications

Experimental hierarchy of two-qubit quantum correlations without state tomography

Experimental hierarchy of two-qubit quantum correlations without state tomography

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

Relating EPR steering with the fidelity of quantum teleportation for two- and three-qubit states

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