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arXiv:1112.4153 · Physical Review A

Using macroscopic entanglement to close the detection loophole in Bell-inequality tests

Youngrong Lim, Mauro Paternostro, Minsu Kang, Jinhyoung Lee, Hyunseok Jeong

Published Jun 19, 2012• 17 citations
arXivHTMLPDF

Abstract

We consider a Bell-like inequality performed using various instances of multiphoton entangled states to demonstrate that losses occurring after the unitary transformations used in the nonlocality test can be counteracted by enhancing the size of such entangled states. In turn, this feature can be used to overcome detection inefficiencies affecting the test itself: a slight increase in the size of such states, pushing them towards a more macroscopic form of entanglement, significantly improves the state robustness against detection inefficiency, thus easing the closing of the detection loophole. Differently, losses before the unitary transformations cause decoherence effects that cannot be compensated using macroscopic entanglement.

DOI
10.1103/physreva.85.062112

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We consider a Bell-like inequality performed using various instances of multiphoton entangled states to demonstrate that losses occurring after the unitary transformations used in the nonlocality test can be counteracted by enhancing the size of such entangled states. In turn, this feature can be used to overcome detection inefficiencies affecting the test itself: a slight increase in the size of such states, pushing them towards a more macroscopic form of entanglement, significantly improves the state robustness against detection inefficiency, thus easing the closing of the detection loophole. Differently, losses before the unitary transformations cause decoherence effects that cannot be compensated using macroscopic entanglement.
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.
We investigate the feasibility of a non-locality test in a bipartite system composed of a single-photon and a multi-photon field that embodies the paradigm of a microscopic-macroscopic entangled state. We run an intrinsically hybrid test requiring polarization measurements on the microscopic part of the state and phase-space ones on the macroscopic counterpart. Our analysis shows that, under ideal conditions, maximal violation of a Bell-CHSH inequality is achievable regardless of the number of photons in the macroscopic part of the state. The difficulty in observing non-locality when losses and detection inefficiency are included can be overcome using a hybrid entanglement witness that allows to efficiently correct for losses in the few photon regime.
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.
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.
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.
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 not sufficiently accurate, they 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 CHSH 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 the micro-macro entanglement in a setup where evidently there is not. By using threshold detectors and postselection, one can only infer the entanglement of the initial pair of photons, so micro-micro entanglement, as it is further confirmed by the violation of a non-separability criterion for bipartite systems. How to detect photonic micro-macro entanglement in the presence of losses with currently available technology remains an open question.