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arXiv:0809.4359 · Physical Review Letters

Proposed Bell Experiment with Genuine Energy-Time Entanglement

Adán Cabello, Alessandro Rossi, Giuseppe Vallone, F. De Martini, Paolo Mataloni

Published Jan 26, 2009• 77 citations
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Abstract

Franson's Bell experiment with energy-time entanglement [Phys. Rev. Lett. 62, 2205 (1989)10.1103/PhysRevLett.62.2205] does not rule out all local hidden variable models. This defect can be exploited to compromise the security of Bell inequality-based quantum cryptography. We introduce a novel Bell experiment using genuine energy-time entanglement, based on a novel interferometer, which rules out all local hidden variable models. The scheme is feasible with actual technology.

DOI
10.1103/physrevlett.102.040401

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Franson's Bell experiment with energy-time entanglement [Phys. Rev. Lett. 62, 2205 (1989)10.1103/PhysRevLett.62.2205] does not rule out all local hidden variable models. This defect can be exploited to compromise the security of Bell inequality-based quantum cryptography. We introduce a novel Bell experiment using genuine energy-time entanglement, based on a novel interferometer, which rules out all local hidden variable models. The scheme is feasible with actual technology.
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.
The Franson interferometer, proposed in 1989 (Franson 1989 Phys. Rev. Lett. 6 2 2205–08 ), beautifully shows the counter-intuitive nature of light. The quantum description predicts sinusoidal interference for specific outcomes of the experiment, and these predictions can be verified in experiment. In the spirit of Einstein, Podolsky, and Rosen it is possible to ask if the quantum-mechanical description (of this setup) can be considered complete. This question will be answered in detail in this paper, by delineating the quite complicated relation between energy-time entanglement experiments and Einstein–Podolsky–Rosen (EPR) elements of reality. The mentioned sinusoidal interference pattern is the same as that giving a violation in the usual Bell experiment. Even so, depending on the precise requirements made on the local realist model, this can imply (a) no violation, (b) smaller violation than usual, or (c) full violation of the appropriate statistical bound. Alternatives include (a) using only the measurement outcomes as EPR elements of reality, (b) using the emission time as EPR element of reality, (c) using path realism, or (d) using a modified setup. This paper discusses the nature of these alternatives and how to choose between them. The subtleties of this discussion needs to be taken into account when designing and setting up experiments intended to test local realism. Furthermore, these considerations are also important for quantum communication, for example in Bell-inequality-based quantum cryptography, especially when aiming for device independence. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
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.
While entanglement and violation of Bell inequalities were initially thought to be equivalent quantum phenomena, we now have different examples of entangled states whose correlations can be described by local hidden--variable models and, therefore, do not violate any Bell inequality. We provide an up to date overview of the existing local hidden--variable models for entangled quantum states, both in the bipartite and multipartite case, and discuss some of the most relevant open questions in this context. Our review covers twenty five years of this line of research since the seminal work by Werner [R. F. Werner, Phys. Rev. A 40, 8 (1989)] providing the first example of an entangled state with a local model, which in turn appeared twenty five years after the seminal work by Bell [J. S. Bell, Physics 1, 195 (1964)], about the impossibility of recovering the predictions of quantum mechanics using a local hidden--variables theory.
Quantum entanglement is an essential principle in quantum mechanics, illustrating the relationship between two or more spatially separated particles.This correlation has been experimentally proven through various techniques, including the entangled photon experiment. Furthermore, the breach of Bell's inequality has confirmed that entanglement represents a genuine physical occurrence, which cannot be accounted for by local hidden variables, thus highlighting the peculiar characteristics of quantum mechanics. This article aims to introduce quantum entanglement and Bell's inequality, and to discuss the experiments conducted by Alain Aspect, John Clauser, and Anton Zeilinger, which paved the way for the development of quantum information science. Additionally, this paper will explore the potential applications of quantum technology in communication, cryptography, and computing, which rely on the exceptional properties of entanglement.