Geometric Bell-like inequalities for steering

Żukowski, Marek; Dutta, Arijit; Yin, Zhi

doi:10.1103/physreva.91.032107

Cited by 62 publications

(50 citation statements)

References 13 publications

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“…But none of these states can violate the steering inequality(Eq. (22) in [18]) and hence may not be steerable in the scenario introduced in [18]. This in turn points out the utility of conditional steerability over the stronger notion of tripartite steerability [18].…”

Section: Tripartite Steering May Not Be Necessary For Conditional mentioning

confidence: 97%

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Conditional steering under the von Neumann scenario

et al. 2017

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In [Phys. Lett. A 166, 293 (1992)] Popescu characterized nonlocality of pure n-partite entangled systems by studying bipartite violation of local realism when n − 2 number of parties perform projective measurements on their particles. A pertinent question in this scenario is whether similar characterization is possible for n-partite mixed entangled states also. In the present work we have followed an analogous approach so as to explore whether given a tripartite mixed entangled state the conditional bipartite states obtained by performing projective measurement on the third party, demonstrate a weaker form of nonlocality, quantum steering. We also compare this new phenomenon of conditional steering with existing notions of tripartite correlations. Interestingly the tripartite state need not be genuinely entangled to demonstrate conditional steering.

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Section: Tripartite Steering May Not Be Necessary For Conditional mentioning

confidence: 97%

“…Using basic geometric approach in [22], Zukowski et.al. showed that the quantum state(ρ AB ) shared between Alice and Bob is steerable(from Alice to Bob) if the corresponding correlation functions satisfy the following inequality:…”

Section: B Steering Criteriamentioning

confidence: 99%

Conditional steering under the von Neumann scenario

et al. 2017

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“…Indeed, the violation of BI has been verified undoubtedly in various systems, for example, with entangled photons [13][14][15], trapped ions [16] and switchable Josephson qubits [17]. Soon after the Bell's pioneer work the original BI was modified to various new forms [32][33][34][35][36][37][38], among which a more suitable inequality for the quantitative test was formulated by Clauser-Horne-Shimony-Holt (CHSH). The entanglement and BI have been also investigated in optical cavity with identical atoms [39][40][41][42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Entanglement dynamics for two spins in an optical cavity – field interaction induced decoherence and coherence revival

Bai¹,

Gao²,

Li³

et al. 2017

Opt. Express

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Abstract:We in this paper study quantum correlations for two neutral spin-particles coupled with a single-mode optical cavity through the usual magnetic interaction. Two-spin entangled states for both antiparallel and parallel spin-polarizations are generated under the photon coherent-state assumption. Based on the quantum master equation we derive the time-dependent quantum correlation of Clauser-Horne-Shimony-Holt (CHSH) type explicitly in comparison with the well known entanglement-measure concurrence. In the two-spin singlet state, which is recognized as one eigenstate of the system, the CHSH correlation and concurrence remain in their maximum values invariant with time and independent of the average photon-numbers either. The correlation varies periodically with time in the general entangled-states for the low average photon-numbers. When the photon number increases to a certain value the oscillation becomes random and the correlations are suppressed below the Bell bound indicating the decoherence of the entangled states. In the high photon-number limit the coherence revivals periodically such that the CHSH correlation approaches the upper bound value at particular time points associated with the cavity-field period.

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“…That is, there exist twoqubit entangled states in which the steerability from two directions are not equivalent (the ability of Alice to steer Bob is not equal to the ability of Bob to steer Alice). The EPR steering can be detected by the violation of various steering inequalities, including linear steering inequalities [14,15], inequalities based on entropic uncertainty relations [16][17][18][19], and steering criterion from geometric Bell-like inequality [20]. On the theory side, based on the choices of measurements, the EPR steering have been explored from projective measurements [13,21] to positive operator-valued measures (POVMs) [22][23][24], and also from continuous variable systems [25,26] to discrete systems [13,21,23] .…”

mentioning

confidence: 99%

“…20]. Here, m · σ A and n · σ B are projective measurements implemented by Alice and Bob, respectively.…”

mentioning

confidence: 99%

Experimental observation of Einstein-Podolsky-Rosen steering via entanglement detection

et al. 2020

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The Einstein-Podolsky-Rosen (EPR) steering is an intermediate quantum nonlocality between entanglement and Bell nonlocality, which plays an important role in quantum information processing tasks. In the past few years, the investigations concerning EPR steering have been demonstrated in a series of experiments. However, these studies rely on the relevant steering inequalities and the choices of measurement settings. Here, we experimentally verify the EPR steering via entanglement detection without using any steering inequality and measurement setting. By constructing two new states from a two-qubit target state, we observe the EPR steering by detecting the entanglement of these new states. The results show that the entanglement of the newly constructed states can be regarded as a new kind of steering witness for target states. Compared to the results of Xiao et al. [Phys. Rev. Lett. 118, 140404 (2017)], we find that the ability of detecting EPR steering in our scenario is stronger than two-setting projective measurements, which can observe more steerable states. Hence, our demonstrations can deepen the understanding of the connection between the EPR steering and entanglement. arXiv:1912.05755v2 [quant-ph]

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Geometric Bell-like inequalities for steering

Cited by 62 publications

References 13 publications

Conditional steering under the von Neumann scenario

Conditional steering under the von Neumann scenario

Entanglement dynamics for two spins in an optical cavity – field interaction induced decoherence and coherence revival

Experimental observation of Einstein-Podolsky-Rosen steering via entanglement detection

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