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arXiv:1304.7460 · Physical Review A

Towards loophole-free Bell inequality test with preselected unsymmetrical singlet states of light

Magdalena Stobińska, Falk Töppel, Pavel Sekatski, Adam Buraczewski

Published Feb 21, 2014• 9 citations
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Abstract

Can a Bell test with no detection loophole be demonstrated for multiphoton entangled states of light within the current technology? We examine the possibility of a postselection-free Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality test with an unsymmetrical polarization singlet. To that end we employ a preselection procedure which is performed prior to the test. It allows using imperfect (coarse-grained) binary photodetection in the test. We show an example of a preselection scheme which improves violation of the CHSH inequality with the micro-macro polarization singlet produced by the optimal quantum cloning. The preselection is realized by a quantum filter which is believed not to be useful for this purpose.

DOI
10.1103/physreva.89.022119

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Can a Bell test with no detection loophole be demonstrated for multiphoton entangled states of light within the current technology? We examine the possibility of a postselection-free Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality test with an unsymmetrical polarization singlet. To that end we employ a preselection procedure which is performed prior to the test. It allows using imperfect (coarse-grained) binary photodetection in the test. We show an example of a preselection scheme which improves violation of the CHSH inequality with the micro-macro polarization singlet produced by the optimal quantum cloning. The preselection is realized by a quantum filter which is believed not to be useful for this purpose.
Quantum correlations may violate the Bell inequalities. Most experimental schemes confirming this prediction have been realized in all-optical Bell tests suffering from the detection loophole. Experiments which simultaneously close this loophole and the locality loophole are highly desirable and remain challenging. An approach to loophole-free Bell tests is based on amplification of the entangled photons (i.e., on macroscopic entanglement), for which an optical signal should be easy to detect. However, the macroscopic states are partially indistinguishable by classical detectors. An interesting idea to overcome these limitations is to replace the postselection by an appropriate preselection immediately after the amplification. This is in the spirit of state preprocessing revealing hidden nonlocality. Here, we examine one of the possible preselections, but the presented tools can be used for analysis of other schemes. Filtering methods making the macroscopic entanglement useful for Bell tests and quantum protocols are the subject of an intensive study in the field nowadays.
The experimental verification of quantum features, such as entanglement, at large scales is extremely challenging because of environment-induced decoherence. Indeed, measurement techniques for demonstrating the quantumness of multiparticle systems in the presence of losses are difficult to define, and if they are not sufficiently accurate they can provide wrong conclusions. We present a Bell test where one photon of an entangled pair is amplified and then detected by threshold detectors, whose signals undergo postselection. The amplification is performed by a classical machine, which produces a fully separable micro–macro state. However, by adopting such a technique one can surprisingly observe a violation of the Clauser–Horne–Shimony–Holt inequality. This is due to the fact that ignoring the detection loophole opened by the postselection and the system losses can lead to misinterpretations, such as claiming micro–macro entanglement in a setup where evidently it is not present. By using threshold detectors and postselection, one can only infer the entanglement of the initial pair of photons, and so micro–micro entanglement, as is further confirmed by the violation of a nonseparability criterion for bipartite systems. How to detect photonic micro–macro entanglement in the presence of losses with the currently available technology remains an open question.
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 question whether Quantum Mechanics describes all aspects of both the micro-world of elementary particles and living organisms adequately is still open. A Bell inequality test without locality and detection loopholes will deliver the answer when applied to macroscopic systems. Here we show that an experimentally feasible loophole-free Bell test is possible using only multi-photon polarization entanglement and linear optics. We apply a preselection protocol which produces genuine macroscopic superpositions and entanglement, thus eliminating postselection and dark counts. Such superpositions are usually difficult to generate. Their study paves the way for testing the quantum nature of biological organisms such as plants, viruses and human brain. Our results find application in creating quantum superpositions of living organisms and their manipulation.
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.