Exponentially Decreasing Critical Detection Efficiency for Any Bell Inequality

Miklin, Nikolai; Chaturvedi, Anubhav; Bourennane, Mohamed; Pawłowski, Marcin; Cabello, Adán

doi:10.1103/physrevlett.129.230403

Cited by 14 publications

(18 citation statements)

References 56 publications

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“…They obtained the following upper bounds for η crit : 0.809 for N = 2 (which is equivalent to d = 4), 0.740 for N = 3 (which is equivalent to d = 8), and 0.693 for N = 4 (which is equivalent to d = 16). More recently, Miklin et al have reported a method that allows us to reduce η crit down to ≈ 0.469 for d = 512 [28].…”

Section: Previous Work 21 Existing Values Of η Critmentioning

confidence: 99%

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Graph-theoretic approach to Bell experiments with low detection efficiency

Steinberg

Singh

et al. 2023

Quantum

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Bell inequality tests where the detection efficiency is below a certain threshold ηcrit can be simulated with local hidden-variable models. Here, we introduce a method to identify Bell tests requiring low ηcrit and relatively low dimension d of the local quantum systems. The method has two steps. First, we show a family of bipartite Bell inequalities for which, for correlations produced by maximally entangled states, ηcrit can be upper bounded by a function of some invariants of graphs, and use it to identify correlations that require small ηcrit. We present examples in which, for maximally entangled states, ηcrit≤0.516 for d=16, ηcrit≤0.407 for d=28, and ηcrit≤0.326 for d=32. We also show evidence that the upper bound for ηcrit can be lowered down to 0.415 for d=16 and present a method to make the upper bound of ηcrit arbitrarily small by increasing the dimension and the number of settings. All these upper bounds for ηcrit are valid (as it is the case in the literature) assuming no noise. The second step is based on the observation that, using the initial state and measurement settings identified in the first step, we can construct Bell inequalities with smaller ηcrit and better noise robustness. For that, we use a modified version of Gilbert's algorithm that takes advantage of the automorphisms of the graphs used in the first step. We illustrate its power by explicitly developing an example in which ηcrit is 12.38% lower and the required visibility is 14.62% lower than the upper bounds obtained in the first step. The tools presented here may allow for developing high-dimensional loophole-free Bell tests and loophole-free Bell nonlocality over long distances.

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Section: Previous Work 21 Existing Values Of η Critmentioning

confidence: 99%

“…Figure 4: η crit as a function of the dimension d of the local system. The previous smallest values are those in[21,26,28] and use nonmaximally entangled states. Pauli (Newman) states refer to the case in which the local measurements are projectors on the Pauli (Newman) states and the initial state is maximally entangled, as described in Sec.…”

mentioning

confidence: 99%

Graph-theoretic approach to Bell experiments with low detection efficiency

Steinberg

Singh

et al. 2023

Quantum

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“…( 15) could also be written as W ρ observed , we found that it is more instructive to give a full expansion of the witness in Eq. (15). Alternatively to defining the state ρ observed in Eq.…”

Section: Discard Strategymentioning

confidence: 99%

“…Here we provide an explicit solution to the SDP in Eq. (15) for the Bell witness W π 4 . This solution, more precisely the minimal value that W π 4 can take for a given η, is shown in Fig.…”

Section: Appendix a Discard Strategy For The Bell Witnessmentioning

confidence: 99%

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Entanglement witnessing with untrusted detectors

Viola¹,

Miklin²,

Gachechiladze³

et al. 2023

Preprint

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We consider the problem of entanglement detection in the presence of faulty, potentially malicious detectors. A common-and, as of yet, the only-approach to this problem is to perform a Bell test in order to identify nonlocality of the measured entangled state. However, there are two significant drawbacks in this approach: the requirement to exceed a critical, and often high, detection efficiency, and much lower noise tolerance. In this paper, we propose an alternative approach to this problem, which is resilient to the detection loophole and is based on the standard tool of entanglement witness. We discuss how the two main techniques to detection losses, namely the discard and assignment strategies, apply to entanglement witnessing. We demonstrate using the example of a two-qubit Bell state that the critical detection efficiency can be significantly reduced compared to the Bell test approach.

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The Schmidt Rank for the Commuting Operator Framework

van Luijk,

Schwonnek,

Stottmeister

et al. 2024

Commun. Math. Phys.

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In quantum information theory, the Schmidt rank is a fundamental measure for the entanglement dimension of a pure bipartite state. Its natural definition uses the Schmidt decomposition of vectors on bipartite Hilbert spaces, which does not exist (or at least is not canonically given) if the observable algebras of the local systems are allowed to be general C*-algebras. In this work, we generalize the Schmidt rank to the commuting operator framework where the joint system is not necessarily described by the minimal tensor product but by a general bipartite algebra. We give algebraic and operational definitions for the Schmidt rank and show their equivalence. We analyze bipartite states and compute the Schmidt rank in several examples: the vacuum in quantum field theory, Araki–Woods-Powers states, as well as ground states and translation invariant states on spin chains which are viewed as bipartite systems for the left and right half chains. We conclude with a list of open problems for the commuting operator framework.

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Exponentially Decreasing Critical Detection Efficiency for Any Bell Inequality

Cited by 14 publications

References 56 publications

Graph-theoretic approach to Bell experiments with low detection efficiency

Graph-theoretic approach to Bell experiments with low detection efficiency

Entanglement witnessing with untrusted detectors

The Schmidt Rank for the Commuting Operator Framework

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