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arXiv:0912.4419 · Physical Review A

Multiparty multilevel energy-time entanglement

Giuseppe Vallone, Paolo Mataloni, Adán Cabello

Published Mar 5, 2010• 5 citations
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Abstract

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 $N$-qubit and $N$-qu$N$it cases. In addition, the proposed setups allow us to prepare and test $N$-qubit Greenberger-Horne-Zeilinger and $({\ensuremath{\sum}}_{i=1}^{N}|i\dots{}i\ensuremath{\rangle})/\sqrt{N}$ energy-time entangled states.

DOI
10.1103/physreva.81.032105

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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∑i=1N∣i…i\ensuremath⟩)/N({\ensuremath{\sum}}_{i=1}^{N}|i\dots{}i\ensuremath{\rangle})/\sqrt{N}(\ensuremath∑i=1N​∣i…i\ensuremath⟩)/N​ energy-time entangled states.
This paper discusses energy-time entanglement experiments and their relation to Einstein-Podolsky-Rosen (EPR) elements of reality.The interferometric experiment proposed by J. D. Franson in 1989 provides the background, and the main issue here is a detailed discussion on whether a Local Realist model can give the Quantum-Mechanical predictions for this setup.The Franson interferometer gives the same interference pattern as the usual Bell experiment (modulo postselection).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.This paper discusses what requirements are necessary on the model to reach a violation, and the motivation for making these requirements.The alternatives include using a) only the measurement outcomes as EPR elements of reality, b) the emission time as EPR element of reality, and c) path realism.The subtleties of this discussion needs to be taken into account when designing and setting up future experiments of this kind, intended to test Local Realism.
It is widely appreciated, due to Bell's theorem, that quantum phenomena are inconsistent with local-realist models. In this context, locality refers to local causality, and there is thus an open possibility for reproducing the quantum predictions with models which internally violate the causal arrow of time, while otherwise adhering to the relevant locality condition. So far, this possibility has been demonstrated only at a toy-model level, and only for systems involving one or two spins (or photons). The present work extends one of these models to quantum correlations between three or more spins which are entangled in the Greenberger-Horne-Zeilinger state.
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.