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arXiv:1208.0622 · Physical Review A

Closing the detection loophole in multipartite Bell tests using Greenberger-Horne-Zeilinger states

Károly F. Pál, Tamás Vértesi, Nicolas Brunner

Published Dec 19, 2012• 15 citations
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Abstract

We investigate the problem of closing the detection loophole in multipartite Bell tests, and show that the required detection efficiencies can be significantly lowered compared to the bipartite case. In particular, we present Bell tests based on $n$-qubit Greenberger-Horne-Zeilinger states, which can tolerate efficiencies as low as $38%$ for a reasonable number of parties and measurements. Even in the presence of a significant amount of noise, efficiencies below $50%$ can be tolerated, which is encouraging given recent experimental progress. Finally, we give strong evidence that, for a sufficiently large number of parties and measurements, arbitrarily small efficiencies can be tolerated, even in the presence of an arbitrary large amount of noise.

DOI
10.1103/physreva.86.062111

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•Nov 1, 2019•15 citations
We investigate the problem of closing the detection loophole in multipartite Bell tests, and show that the required detection efficiencies can be significantly lowered compared to the bipartite case. In particular, we present Bell tests based on nnn-qubit Greenberger-Horne-Zeilinger states, which can tolerate efficiencies as low as 3838%38 for a reasonable number of parties and measurements. Even in the presence of a significant amount of noise, efficiencies below 5050%50 can be tolerated, which is encouraging given recent experimental progress. Finally, we give strong evidence that, for a sufficiently large number of parties and measurements, arbitrarily small efficiencies can be tolerated, even in the presence of an arbitrary large amount of noise.
We show that the detection efficiencies required for closing the detection loophole in Bell tests can be significantly lowered using quantum systems of dimension larger than two. We introduce a series of asymmetric Bell tests for which an efficiency arbitrarily close to 1/N can be tolerated using N-dimensional systems, and a symmetric Bell test for which the efficiency can be lowered down to 61.8% using four-dimensional systems. Experimental perspectives for our schemes look promising considering recent progress in atom-photon entanglement and in photon hyperentanglement.
We study the problem of closing the detection loophole in three-qubit Bell tests, the experimentally most relevant case beyond the usual bipartite scenario, and show that the minimal detection efficiencies required can be considerably lowered compared to the two-qubit case. The lowest reported detection efficiency thresholds for two and three qubits so far are $\ensuremath{\sim}66.7$ and 6060%60, respectively. Using the three-qubit WWW state and a three-setting Bell inequality, we beat these thresholds and with an eight-setting Bell inequality we reach 50.1350.13%50.13. We also investigate generic three-qubit states which allow us to attain a detection efficiency of 5050%50 in a four-setting Bell test. We conjecture that the limit of 5050%50 is unbeatable using three-qubit states and any number of measurements.
Device-independent certification schemes have gained a lot of interest lately, not only for their applications in quantum information tasks, but also their implications towards foundations of quantum theory. The strongest form of device-independent certification, known as self-testing, often requires for a Bell inequality to be maximally violated by specific quantum states and measurements. In this work, using the techniques developed recently [S. Sarkar et al., npj Quantum Inf. 7, 151 (2021)], we provide a self-testing scheme for the multipartite Greenberger-Horne-Zeilinger states of arbitrary local dimension that does not rely on self-testing results for qubit states and that exploits the minimal number of two measurements per party. This makes our results interesting as far as practical implementation of device-independent certification methods is concerned. Our self-testing statement relies on maximal violation of a Bell inequality proposed recently [R. Augusiak et al., New J. Phys. 21, 113001 (2019)].
Abstract In device-independent quantum information processing Bell inequalities are not only used as detectors of nonlocality, but also as certificates of relevant quantum properties. In order for these certificates to work, one very often needs Bell inequalities that are maximally violated by specific quantum states. Recently, in Salavrakos et al (2017 Phys. Rev. Lett. 119 040402) a general class of Bell inequalities, with arbitrary numbers of measurements and outcomes, has been designed, which are maximally violated by the maximally entangled states of two quantum systems of arbitrary dimension. In this work, we generalize these results to the multipartite scenario and obtain a general class of Bell inequalities maximally violated by the Greenberger–Horne–Zeilinger states of any number of parties and any local dimension. We then derive analytically their maximal quantum and nonsignaling values. We also obtain analytically the bound for detecting genuine nonlocality and compute the fully local bound for a few exemplary cases. Moreover, we consider the question of adapting this class of inequalities to partially entangled Greenberger–Horne–Zeilinger-like states for some special cases of low dimension and small number of parties. Through numerical methods, we find classes of inequalities maximally violated by these partially entangled states.
Abstract In device-independent quantum information processing Bell inequalities are not only used as detectors of nonlocality, but also as certificates of relevant quantum properties. In order for these certificates to work, one very often needs Bell inequalities that are maximally violated by specific quantum states. Recently, in Salavrakos et al (2017 Phys. Rev. Lett. 119 040402) a general class of Bell inequalities, with arbitrary numbers of measurements and outcomes, has been designed, which are maximally violated by the maximally entangled states of two quantum systems of arbitrary dimension. In this work, we generalize these results to the multipartite scenario and obtain a general class of Bell inequalities maximally violated by the Greenberger–Horne–Zeilinger states of any number of parties and any local dimension. We then derive analytically their maximal quantum and nonsignaling values. We also obtain analytically the bound for detecting genuine nonlocality and compute the fully local bound for a few exemplary cases. Moreover, we consider the question of adapting this class of inequalities to partially entangled Greenberger–Horne–Zeilinger-like states for some special cases of low dimension and small number of parties. Through numerical methods, we find classes of inequalities maximally violated by these partially entangled states.