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arXiv:1110.3721 · Physical Review A

Feasibility of loophole-free nonlocality tests with a single photon

Rafael Chaves, Jonatan Bohr Brask

Published Dec 19, 2011• 28 citations
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Abstract

Recently, much interest has been directed toward designing setups that achieve realistic loss thresholds for decisive tests of local realism---in particular in the optical regime. We analyze the feasibility of such Bell tests based on a $W$ state shared between multiple parties, which can be realized, for example, by a single photon shared between spatial modes. We develop a general error model to obtain thresholds for the efficiencies required to violate local realism and also consider two concrete optical-measurement schemes.

DOI
10.1103/physreva.84.062110

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Recently, much interest has been directed toward designing setups that achieve realistic loss thresholds for decisive tests of local realism---in particular in the optical regime. We analyze the feasibility of such Bell tests based on a WWW state shared between multiple parties, which can be realized, for example, by a single photon shared between spatial modes. We develop a general error model to obtain thresholds for the efficiencies required to violate local realism and also consider two concrete optical-measurement schemes.
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Loophole-free quantum nonlocality often demands experiments with high complexity (defined by all parties' settings and outcomes) and multiple efficient detectors. Here, we identify the fundamental efficiency and complexity thresholds for quantum steering using two-qubit entangled states. Remarkably, it requires only one photon detector on the untrusted side, with efficiency ε>1/Xε> 1/Xε>1/X, where X≥2X \geq 2X≥2 is the number of settings on that side. This threshold applies to all pure entangled states, in contrast to analogous Bell-nonlocality tests, which require almost unentangled states to be loss-tolerant. We confirm these predictions in a minimal-complexity (X=2X = 2X=2 for the untrusted party and a single three-outcome measurement for the trusted party), detection-loophole-free photonic experiment with $ε= (51.6 \pm 0.4)\% $.
We present a loophole-free violation of local realism using entangled photon pairs. We ensure that all relevant events in our Bell test are spacelike separated by placing the parties far enough apart and by using fast random number generators and high-speed polarization measurements. A high-quality polarization-entangled source of photons, combined with high-efficiency, low-noise, single-photon detectors, allows us to make measurements without requiring any fair-sampling assumptions. Using a hypothesis test, we compute p values as small as 5.9×10^{-9} for our Bell violation while maintaining the spacelike separation of our events. We estimate the degree to which a local realistic system could predict our measurement choices. Accounting for this predictability, our smallest adjusted p value is 2.3×10^{-7}. We therefore reject the hypothesis that local realism governs our experiment.
The question of testing the nonlocality of a single photon has raised much debate over the last years. The controversy is intimately related to the issue of providing a common reference frame for the observers to perform their local measurements. Here we address this point by presenting a simple scheme for demonstrating the nonlocality of a single photon which does not require a shared reference frame. Specifically, Bell inequality violation can be obtained with certainty with unaligned devices, even if the relative frame fluctuates between each experimental run of the Bell test. Our scheme appears feasible with current technology and may simplify the realization of quantum communication protocols based on single-photon entanglement.
Abstract Bell’s inequality provides a remarkable way to test the consistency between quantum mechanics and classic local realistic theory. However, experimental demonstrations of the loophole-free Bell test are challenging and only recently have been demonstrated with bipartite systems. A central obstacle for the photonic system is that the sampling efficiency, including the collection and detection efficiencies, must be above a certain threshold. We here generalize two-particle Eberhard’s inequality to the n-particle systems and derive a Bell-type inequality for multi-particle systems, which significantly relaxes this threshold. Furthermore, an experimental proposal to achieve a multi-partite Bell test without the fair sampling assumption is presented for the case of three particles. For any given value of the sampling efficiency, we give the optimal configurations for actual implementation, the optimal state, the maximum background noise that the system can tolerate, and the lowest fidelity of the quantum state. We believe our work can serve as a recipe for experimentalists planning to violate local realism using a multi-partite quantum state without the sampling loophole.
It is shown that a loophole-free Bell test can be achieved using continuous variables of light. A feasible optical setup is proposed for this purpose, based on a non-Gaussian state of light and high-efficiency homodyne detectors. The non-Gaussian entangled state can be generated from a two-mode squeezed vacuum state by subtracting a single photon from each mode using beam splitters and standard low-efficiency single-photon detectors. A Bell violation exceeding 1% can be attained with 6 dB squeezed light and an homodyne efficiency around 95%. A detailed feasibility analysis, including the effect of the detector efficiency, the electronic noise, the impurity of the non-Gaussian state, and the probability of false triggers, suggests that this method opens a promising avenue towards a complete experimental Bell test.