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Violation of Bell's inequality using imperfect photodetectors with optical hybrid entanglement

Hyukjoon Kwon, Hyunseok Jeong

Published Sep 9, 2013• 0 citations
OpenAlex

Abstract

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.

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The tests of Bell's inequality to date have failed to be definitive because of the ``detection loophole,'' due to the inefficiency of photodetectors. An idealized experiment using pairs of two-level Rydberg atoms, correlated with the help of a quantized cavity field, was proposed by Oliver and Stroud [J. Opt. Soc. Am. B 4, 1426 (1987)] for the purpose of blocking this loophole. We develop their proposal by removing their idealizations. We carefully define the ensemble of atom pairs by imposing conditions on arrival times at the analyzers of the atoms. We take into account the spread of velocities of the atoms, which implies that the ensemble must be described quantum mechanically by a statistical operator rather than a pure state, and we show that with detector efficiencies of 0.9 or better, quantum mechanics implies a strong violation of Bell's inequality in the ensemble. Upper and lower bounds on ensemble averages can be inferred from experimental averages, thereby permitting an experimental test of Bell's inequality in the ensemble. \textcopyright{} 1996 The American Physical Society.

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Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.

•Dec 1, 2009•29 citations
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 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.
Abstract Optical hybrid entanglement can be created between two qubits, one encoded in a single photon and another one in coherent states with opposite phases. It opens the path to a variety of quantum technologies, such as heterogeneous quantum networks, merging continuous- and discrete-variable encoding, and enabling the transport and interconversion of information. However, reliable characterization of the non-local nature of this quantum state is limited so far to full quantum state tomography. Here, we perform a thorough study of Clauser–Horne–Shimony–Holt Bell inequality tests, enabling practical verification of quantum nonlocality for optical hybrid entanglement. We show that a practical violation of this inequality is possible with simple photon number on/off measurements if detection efficiencies stay above 82%. Another approach, based on photon-number parity measurements, requires 94% efficiency but works well in the limit of higher photon populations. Both tests use no postselection of the measurement outcomes and they are free of the fair-sampling hypothesis. Our proposal paves the way to performing loophole-free tests using feasible experimental tasks such as coherent state interference and photon counting.
The violation of Bell inequalities where both detection and locality loopholes are closed is crucial for device-independent assessments of quantum information. While of a technological nature, the simultaneous closing of both loopholes still remains a challenge. In Teo et al. [Nat. Commun. 4, 2104 (2013)], a realistic setup to produce an atom-photon entangled state that could reach a loophole-free Bell inequality violation within current experimental technology is proposed. Here we improve the analysis of this proposal by giving an analytical treatment that shows that the state proposed in Teo et al. [Nat. Commun. 4, 2104 (2013)] can violate a Bell inequality for arbitrarily low photodectection efficiency, when all other losses are ignored. Moreover, it is also able to violate a Bell inequality considering only atomic and homodyne measurements eliminating the need to consider inefficient photocounting measurements. In this case, the maximum Clauser-Horne-Shimony-Holt inequality violation achievable is 2.29, and the minimum transmission required for violation is about 68%. Finally, we show that by postselecting on an atomic measurement, one can engineer superpositions of coherent states for various coherent state amplitudes.
The tests of Bell's inequality to date have failed to be definitive because of the ``detection loophole,'' due to the inefficiency of photodetectors. An idealized experiment using pairs of two-level Rydberg atoms, correlated with the help of a quantized cavity field, was proposed by Oliver and Stroud [J. Opt. Soc. Am. B 4, 1426 (1987)] for the purpose of blocking this loophole. We develop their proposal by removing their idealizations. We carefully define the ensemble of atom pairs by imposing conditions on arrival times at the analyzers of the atoms. We take into account the spread of velocities of the atoms, which implies that the ensemble must be described quantum mechanically by a statistical operator rather than a pure state, and we show that with detector efficiencies of 0.9 or better, quantum mechanics implies a strong violation of Bell's inequality in the ensemble. Upper and lower bounds on ensemble averages can be inferred from experimental averages, thereby permitting an experimental test of Bell's inequality in the ensemble. \textcopyright{} 1996 The American Physical Society.
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.