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Quantum Nonlocality with Arbitrary Limited Detection Efficiency

Abstract : The demonstration and use of nonlocality, as defined by Bell's theorem, rely strongly on dealing with non-detection events due to losses and detectors' inefficiencies. Otherwise, the so-called detection loophole could be exploited. The only way to avoid this is to have detection efficiencies that are above a certain threshold. We introduce the intermediate assumption of limited detection efficiency, that is, in each run of the experiment, the overall detection efficiency is lower bounded by ηmin > 0. Hence, in an adversarial scenario, the adversaries have arbitrary large but not full control over the inefficiencies. We analyse the set of possible correlations that fulfil Limited Detection Locality (LDL) and show that they necessarily satisfy some linear Bell-like inequalities. We prove that quantum theory predicts the violation of one of these inequalities for all ηmin > 0. Hence, non-locality can be demonstrated with arbitrarily small limited detection efficiencies. We validate this assumption experimentally via a twin-photon implementation in which two users are provided with one photon each out of a partially entangled pair. We exploit on each side a passive switch followed by two measurement devices with fixed settings. Assuming the switches are not fully controlled by an adversary, nor by hypothetical local variables, we reveal the nonlocality of the established correlations despite a low overall detection efficiency. Introduction — When studying the discoveries in fundamental physics of the past century, one cannot help but come across Bell's seminal work on the nonlocal nature of quantum theory [1]. It implies that quantum physics can produce correlations which cannot be explained by a common past with local variables propagating contiguously. This has not only proven fascinating from a foundational point of view, but also given rise to applications in device independent quantum information processing (DIQIP) [2], such as quantum key distribution [3–5], randomness generation [6, 7], or entanglement certification [8, 9]. For a semi broad-audience presentation of these concepts, see [10]. Let us briefly recall the concept of local and nonlocal correlations. Assume that a source emits pairs of particles that travel to two distant stations, traditionally called Alice and Bob. As depicted in FIG. 1, the two ex-perimentalists perform one out of several possible measurements on the individual particles they each receive and record the associated outcomes. We denote Alice's and Bob's measurement choices by x and y and their recorded outcomes by a and b, respectively. They can then compute the correlation P (ab|xy). Given the setup, it seems natural to think that any correlations that Alice and Bob can observe in this way are due to particles having a common past, as they come from the same source. We refer to this common past by λ. Correlations that can be explained by the existence of such a parameter are called local : P L (ab|xy) =
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Submitted on : Tuesday, January 12, 2016 - 10:47:31 AM
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Gilles Pütz, Anthony Martin, Nicolas Gisin, Djeylan Aktas, Bruno Fedrici, et al.. Quantum Nonlocality with Arbitrary Limited Detection Efficiency. Physical Review Letters, American Physical Society, 2016, 116, pp.010401. ⟨10.1103/PhysRevLett.116.010401⟩. ⟨hal-01254373⟩



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