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arXiv:1112.1719 · Physical Review A

Tests of Bell inequality with arbitrarily low photodetection efficiency and homodyne measurements

Mateus Araújo, Marco Túlio Quintino, Daniel Cavalcanti, Marcelo França Santos, Adán Cabello, Marcelo Terra Cunha

Published Sep 4, 2012• 13 citations
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Abstract

We show that hybrid local measurements combining homodyne measurements and photodetection provide violations of a Bell inequality with arbitrarily low photodetection efficiency. This is shown in two different scenarios: when one part receives an atom entangled to the field mode to be measured by the other part and when both parts make similar photonic measurements. Our findings promote the hybrid measurement scenario as a candidate for loophole-free Bell tests beyond previous expectations.

DOI
10.1103/physreva.86.030101

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We show that hybrid local measurements combining homodyne measurements and photodetection provide violations of a Bell inequality with arbitrarily low photodetection efficiency. This is shown in two different scenarios: when one part receives an atom entangled to the field mode to be measured by the other part and when both parts make similar photonic measurements. Our findings promote the hybrid measurement scenario as a candidate for loophole-free Bell tests beyond previous expectations.
We show that a Bell inequality test using an optical hybrid state between a polarized single photon and a coherent field can be highly robust against detection inefficiency. The Bell violation occurs until the efficiency becomes as low as 67% even though its degree becomes small as the detection efficiency degrades. We consider on/off and photon number parity measurements, respectively, for the Bell test and they result in the similar conditions. If the detection efficiency is higher than 98.68%, parity measurements give larger Bell violations close to Cirel'son's bound, while on/off measurements give larger but moderate violations for realistic values of detector efficiency. Experimental realization of our proposal seems feasible in the near future for the implementation of a loophole-free Bell inequality test.
We study nonlocality tests in which each party performs photodetection and homodyne measurements. The results of such measurements are dichotomized and a Clauser–Horne–Shimony–Holt inequality is used. We prove that in this scenario the maximal violation is attainable and fully characterize the set of maximally violating states. If we restrict our search to states composed of at most 2, 4 and 6 photons per mode, we find critical photodetection efficiencies of 0.48, 0.36 and 0.29. We also found an entangled variation of the famous cat states that has critical efficiency 0.32. These values are well within the limit of current photodetector technology, which suggests the present approach as a road for a loophole-free Bell experiment.
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We show that a Bell inequality test using an optical hybrid state between a polarized single photon and a coherent field can be highly robust against detection inefficiency. The Bell violation occurs until the efficiency becomes as low as 67% even though its degree becomes small as the detection efficiency degrades. We consider on/off and photon number parity measurements, respectively, for the Bell test and they result in similar conditions. If the detection efficiency is higher than 98.68%, parity measurements give larger Bell violations close to Cirel'son's bound, while on/off measurements give larger but moderate violations for realistic values of detector efficiency. Experimental realization of our proposal seems feasible in the near future for the implementation of a loophole-free Bell inequality test.
We study Bell-inequality tests with entanglement between a coherent-state field in a cavity and a two-level atom. In order to detect the cavity field for such a test, photon on-off measurements and photon number parity measurements, respectively, are investigated. When photon on-off measurements are used, at least 50% of detection efficiency is required to demonstrate violation of the Bell inequality. Photon number parity measurements for the cavity field can be effectively performed using ancillary atoms and an atomic detector, which leads to large degrees of Bell violations up to Cirel'son's bound. We also analyze decoherence effects in both field and atomic modes and discuss conditions required to perform a Bell inequality test free from the locality loophole.