Robust self-testing of the three-qubit<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>W</mml:mi></mml:math>state

Wu, Xingyao; Cai, Yu; Yang, Tzyh Haur; Le, Huy Nguyen; Bancal, Jean-Daniel; Scarani, Valerio

doi:10.1103/physreva.90.042339

Cited by 74 publications

(70 citation statements)

References 23 publications

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“…Other works (e.g., Refs. [31,40,44]) maximizing Bell functionals using the W state rely on the same symmetry considerations. With this simplification, we have two optimization parameters.…”

Section: A Lower Bound For the Persistency Of Nonlocality Of The mentioning

confidence: 99%

Bounding the persistency of the nonlocality ofWstates

et al. 2016

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The nonlocal properties of the W states are investigated under particle loss. By removing all but two particles from an N -qubit W state, the resulting two-qubit state is still entangled. Hence, the W state has high persistency of entanglement. We ask an analogous question regarding the persistency of nonlocality introduced in [Phys. Rev. A 86, 042113]. Namely, we inquire what is the minimal number of particles that must be removed from the W state so that the resulting state becomes local. We bound this value in function of N qubits by considering Bell nonlocality tests with two alternative settings per site. In particular, we find that this value is between 2N/5 and N/2 for large N . We also develop a framework to establish bounds for more than two settings per site.

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“…Other works (e.g., Refs. [31,40,44]) maximizing Bell functionals using the W state rely on the same symmetry considerations. With this simplification, we have two optimization parameters.…”

Section: A Lower Bound For the Persistency Of Nonlocality Of The mentioning

confidence: 99%

Bounding the persistency of the nonlocality ofWstates

et al. 2016

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“…The nonlocality of the simplest Dicke states, featuring a single excitation (the so-called W -states), has been widely discussed [21][22][23][24][25][26][27], in particular in the context of optical Bell tests based on single photon entanglement [28][29][30]. Notably, the possibility of self-testing the W state has been recently demonstrated [31,32]. Finally, the relevance of the nonlocality of Dicke states in the context of manybody physics has been recently discussed [33].…”

Section: Introductionmentioning

confidence: 99%

Nonlocality ofWand Dicke states subject to losses

et al. 2015

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We discuss the nonlocality of the W and the Dicke states subject to losses. We consider two noise models, namely loss of excitations and loss of particles, and investigate how much loss can be tolerated such that the final state remains nonlocal. This leads to a measure of robustness of the nonlocality of Dicke states, with a clear physical interpretation. Our results suggest that the relation between nonlocality and entanglement of Dicke states is not monotonous.

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“…Remarkably, they also find applications in numerous quantum information and communication tasks, e.g., in quantum key distribution involving untrusted devices [6][7][8], in the reduction of communication complexity [9], in the expansion of trusted random numbers [10,11], in certifying the Hilbert space dimension of physical systems [12,13], in self-testing [14][15][16][17][18] of quantum devices, in witnessing [19][20][21] and quantifying [22][23][24][25] (multipartite) quantum entanglement using untrusted devices etc. For a recent review on these and other applications, see [3].…”

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Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth

et al. 2015

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We present a simple family of Bell inequalities applicable to a scenario involving arbitrarily many parties, each of which performs two binary-outcome measurements. We show that these inequalities are members of the complete set of full-correlation Bell inequalities discovered by Werner-WolfZukowski-Brukner. For scenarios involving a small number of parties, we further verify that these inequalities are facet-defining for the convex set of Bell-local correlations. Moreover, we show that the amount of quantum violation of these inequalities naturally manifests the extent to which the underlying system is genuinely many-body entangled. In other words, our Bell inequalities, when supplemented with the appropriate quantum bounds, naturally serve as device-independent witnesses for entanglement depth, allowing one to certify genuine k-partite entanglement in an arbitrary n ≥ k-partite scenario without relying on any assumption about the measurements being performed, nor the dimension of the underlying physical system. A brief comparison is made between our witnesses and those based on some other Bell inequalities, as well as the quantum Fisher information. A family of witnesses for genuine k-partite nonlocality applicable to an arbitrary n ≥ k-partite scenario based on our Bell inequalities is also presented. One of the most important no-go theorems in physics concerns the impossibility to reproduce all quantum mechanical predictions using any locally-causal theory [1] -a fact commonly referred to as Bell's theorem [2]. An important observation leading to this celebrated result is that measurement statistics allowed by such theories must satisfy constraints in the form of an inequality, a Bell inequality. Since these inequalities only involve experimentally accessible quantities, their violation -a manifestation of Bell-nonlocality [3] -can be, and has been (modulo some arguably implausible loopholes [4]) empirically demonstrated (see, e.g., [3][4][5] and references therein).Clearly, Bell inequalities played an instrumental role in the aforementioned discovery. Remarkably, they also find applications in numerous quantum information and communication tasks, e.g., in quantum key distribution involving untrusted devices [6][7][8], in the reduction of communication complexity [9], in the expansion of trusted random numbers [10,11], in certifying the Hilbert space dimension of physical systems [12,13], in self-testing [14-18] of quantum devices, in witnessing [19][20][21] and quantifying [22-25] (multipartite) quantum entanglement using untrusted devices etc. For a recent review on these and other applications, see [3].Identifying interesting or useful Bell inequalities is nonetheless by no means obvious. For instance, the approach of solving for the complete set of optimal, i.e., facet-defining Bell inequalities for a given experimental scenario -though potentially useful for the identification of non-Bell-local (hereafter nonlocal) correlationstypically produces a large number of inequalities with no * yliang@phys.ethz....

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Robust self-testing of the three-qubitWstate

Cited by 74 publications

References 23 publications

Bounding the persistency of the nonlocality ofWstates

Bounding the persistency of the nonlocality ofWstates

Nonlocality ofWand Dicke states subject to losses

Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth

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