Entanglement and communication-reducing properties of noisy<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>-qubit states

Laskowski, Wiesław; Paterek, Tomasz; Brukner, Časlav; Żukowski, Marek

doi:10.1103/physreva.81.042101

Cited by 22 publications

(32 citation statements)

References 47 publications

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“…Let us subtract the conjectured β c,n (19) from I(a, b, c, d) in formula (32). Notice that we end the proof once we find that β c,n − I(a, b, c, d) ≥ 0 for all possible positive integers a, b, c, d…”

Section: A Family Of Two-setting Multipartite Bell Inequalitiesmentioning

confidence: 98%

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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Section: A Family Of Two-setting Multipartite Bell Inequalitiesmentioning

confidence: 98%

Bounding the persistency of the nonlocality ofWstates

et al. 2016

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“…The qubits are distributed over channels that introduce a level γ ∈ [0, 1] of local depolarizing noise, where γ = 1 corresponds to no noise. Regardless of its physical origin, local depolarizing noise can be modeled by reducing the visibility of the measurements at each site as γΩ [11]. We do not consider colored noise, such as local dephasing noise, as such noise models could allow the parties to establish some common direction.…”

Section: Arxiv:11111864v3 [Quant-ph] 6 Feb 2012mentioning

confidence: 99%

Observers can always generate nonlocal correlations without aligning measurements by covering all their bases

Wallman

Bartlett

2012

Phys. Rev. A

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Quantum theory allows for correlations between the outcomes of distant measurements that are inconsistent with any locally causal model, as demonstrated by the violation of a Bell inequality. Typical demonstrations of these correlations require careful alignment between the measurements, which requires distant parties to share a reference frame. Here, we prove, following a numerical observation by Shadbolt et al., that if two parties share a Bell state and each party preforms measurements along three perpendicular directions on the Bloch sphere, then the parties will always violate a Bell inequality. Furthermore, we prove that this probability is highly robust against local depolarizing noise, in that small levels of noise only decrease the probability of violating a Bell inequality by a small amount. We also show that generalizing to N parties can increase the robustness against noise. These results improve on previous ones that only allowed a high probability of violating a Bell inequality for large numbers of parties. One of the most fascinating and useful features of quantum theory is that the correlations between the outcomes of spatially separated measurements can be nonlocal, i.e., inconsistent with any locally causal model [1,2]. Typically, to obtain nonlocal correlations experimentally, great care is taken to choose measurements that give the strongest nonlocal correlations possible, which requires distant parties to share a reference frame [3,4]. While there are proposals for violating a Bell inequality without the need for a prior shared reference frame [4,5], these proposals add substantial complexity to the simple form of a standard Bell test.Distant parties could attempt to violate a Bell inequality without aligning reference frames by performing measurements in random directions [6][7][8], and recent results prove that such a method can demonstrate a violation with some nonzero probability. Specifically, for N spatially-separated parties who share a GreenbergerHorne-Zeilinger (GHZ) state [9], almost all choices of two measurements at each site lead to nonlocal correlations between measurement outcomes if the number of parties N is large [7]. Therefore distant parties that do not share a reference frame can randomly choose measurements that violate some Bell inequality with a probability that approaches 1 as N increases. If the parties also share a single direction on the Bloch sphere (as can be the case in, e.g., photon polarization encodings [4]), then they can always violate one of two Bell inequalities by an amount that is exponential in N [8].These results are the weakest for the scenario most relevant to experiments, namely, the bipartite N = 2 case: the probability of violating a Bell inequality by choosing two mutually unbiased measurements randomly in the bipartite case is ∼ 42% [7]. In this paper, we show that if the two parties each choose three measurements corresponding to the x, y and z components of their local Cartesian reference frame (hereafter referred to as a triad of measuremen...

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“…For a given Dicke state, our goal is to determine how much loss can be tolerated such that the final state remains nonlocal, i.e. still violates a Bell inequality [34,35]. Our focus is to derive bounds for the case of Dicke states featuring a large number of particles or modes.…”

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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Entanglement and communication-reducing properties of noisyN-qubit states

Cited by 22 publications

References 47 publications

Bounding the persistency of the nonlocality ofWstates

Bounding the persistency of the nonlocality ofWstates

Observers can always generate nonlocal correlations without aligning measurements by covering all their bases

Nonlocality ofWand Dicke states subject to losses

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