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arXiv:1101.5226 · Physical Review A

Testing Hardy’s nonlocality proof with genuine energy-time entanglement

Giuseppe Vallone, Ilaria Gianani, Enrique B. Inostroza, C. Saavedra, G. Lima, Adán Cabello, Paolo Mataloni

Published Apr 18, 2011• 41 citations
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Abstract

We show two experimental realizations of Hardy's ladder test of quantum nonlocality using energy-time correlated photons, following the scheme proposed by Cabello et al.[Phys. Rev. Lett. 102, 040401 (2009)]. Unlike previous energy-time Bell experiments, these tests require precisely tailored nonmaximally entangled states. One of them is equivalent to the two-setting and two-outcome Bell test requiring a minimum detection efficiency. The reported experiments are still affected by the locality and detection loopholes, but are free of the post-selection loophole of previous energy-time and time-bin Bell tests.

DOI
10.1103/physreva.83.042105

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We show two experimental realizations of Hardy's ladder test of quantum nonlocality using energy-time correlated photons, following the scheme proposed by Cabello et al.[Phys. Rev. Lett. 102, 040401 (2009)]. Unlike previous energy-time Bell experiments, these tests require precisely tailored nonmaximally entangled states. One of them is equivalent to the two-setting and two-outcome Bell test requiring a minimum detection efficiency. The reported experiments are still affected by the locality and detection loopholes, but are free of the post-selection loophole of previous energy-time and time-bin Bell tests.
Bell's theorem states that the quantum mechanical description of physical quantities cannot be fully explained by local realistic theories, laying a solid basis for various quantum information applications. Hardy's paradox is celebrated as the simplest form of Bell's theorem concerning its "All versus Nothing" approach to test local realism. However, due to experimental imperfections, existing tests of Hardy's paradox require additional assumptions of the experimental systems, and these assumptions constitute potential loopholes for faithfully testing local realistic theories. Here, we experimentally demonstrate Hardy's nonlocality through a photonic entanglement source. By achieving a detection efficiency of 82.2%, a quantum state fidelity of 99.10%, and applying high-speed quantum random number generators for the measurement setting switching, the experiment is implemented in a loophole-free manner. During 6 h of running, a strong violation of P_{Hardy}=4.646×10^{-4} up to 5 standard deviations is observed with 4.32×10^{9} trials. A null hypothesis test shows that the results can be explained by local realistic theories with an upper bound probability of 10^{-16348}. These testing results provide affirmative evidence against local realism, and establish an advancing benchmark for quantum information applications based on Hardy's paradox.
There are two powerful arguments against the possibility of extending quantum mechanics, the violation of Bell inequalities and the Kochen-Specker theorem, but the connection between the two remains confused. Following the distinctive strategy proposed by Cabello [Phys. Rev. Lett. 127, 070401 (2021)], Bell inequalities can be violated by state-independent contextuality sets. However, the experimental realization of such ideas is challenging as it requires high-dimensional entanglement. Orbital angular momentum provides an unlimited state space and the number of effective dimensions can be readily tailored as required. We performed an experimental test of non-locality based on Bell inequalities from contextuality, using orbital angular momentum entanglement in a bipartite photonic system. Our experiment not only shows a new way to produce non-locality but also connects contextuality and non-locality, two fundamental quantum resources that are critical for quantum computation and secure communication tasks.
Self-testing protocols enable the certification of quantum devices without demanding full knowledge about their inner workings. A typical approach in designing such protocols is based on observing nonlocal correlations which exhibit maximum violation in a Bell test. We show that in the Bell experiment known as Hardy's test of nonlocality, not only does the maximally nonlocal correlation self-test a quantum state, rather a nonmaximal nonlocal behavior can serve the same purpose. We, in fact, completely characterize all such behaviors leading to a self-test of every pure two-qubit entangled state except for the maximally entangled ones. Apart from presenting an alternative self-testing protocol, our method provides a powerful tool towards characterizing the complex boundary of the set of quantum correlations.
The energy-time entangled biphoton source plays a great role in quantum communication, quantum metrology, and quantum cryptography due to its strong temporal correlation and capability of nonlocal dispersion cancellation. As a quantum effect, nonlocal dispersion cancellation is further proposed as an alternative way for nonlocality testing of continuous variable entanglement via the violation of the Bell-like inequality proposed by Wasak et al. [Phys. Rev. A 82, 052120 (2010)]. However, to date there is no experimental report either on the inequality violation or on a nonlocal detection with single-photon detectors at a long-distance transmission channel, which is key for a true nonlocality test. In this paper, we report an experimental realization of a violation of the inequality after 62-km optical fiber transmission at telecom wavelengths with a nonlocal detection based on event timers and a cross-correlation algorithm, which indicates a successful nonlocal test of energy-time entanglement. This work provides feasibility for the strict test of the nonlocality for continuous variables in both long-distance communication fiber channel and free space.
Franson-like setups are inadequate for multiparty Bell experiments with energy-time entanglement because postselected events can depend on the local settings, and local models can exploit this feature to reproduce the quantum predictions, even in the case of ideal devices. We extend a previously introduced interferometric scheme [A. Cabello et al., Phys. Rev. Lett. 102, 040401 (2009)] to solve this problem in the NNN-qubit and NNN-quNNNit cases. In addition, the proposed setups allow us to prepare and test NNN-qubit Greenberger-Horne-Zeilinger and $({\ensuremath{\sum}}_{i=1}^{N}|i\dots{}i\ensuremath{\rangle})/\sqrt{N}$ energy-time entangled states.