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arXiv:1104.4781 · Quantum Information and Computation

On the experimental violation of Mermin's inequality with imperfect measurements

Ruffin E. Evans, Olivier Pfister

Published Sep 1, 2011• 2 citations
arXivHTMLPDF

Abstract

We investigate theoretically the feasibility of an experimental test of the Bell-type inequality derived by Mermin for correlated spins larger than ${1}/{2}$. Using the Schwinger representation, we link the output fields of two two-mode squeezers in order to create correlated effective spins between two observers. Spin measurements will be performed by photon-number-resolved photodetection, which has recently come of age. We examine the effect of nonideal detection quantum efficiency -and any other optical loss - on the violation margin of Mermin's inequality. We find that experimental violation is well accessible for spins larger than 1, for quantum efficiencies compatible with the current state of the art.

DOI
10.26421/qic11.9-10-7

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We show that various experimental configurations using correlated photon-number states are predicted to violate many forms of Bell's inequality. This test is potentially one of macroscopic quantum mechanics in that violations are predicted for situations where large numbers of photons are detected at a single detector at a time. The configurations also allow higher-spin tests of quantum mechanics. We indicate how the violations of Bell inequalities might be achieved with both parametric amplification and parametric oscillation. The effect of photodetection inefficiencies is analyzed. In order to investigate the potential for Bell-inequality tests in the high-intensity regime of recent experiments where detection efficiencies may be very high, we introduce a simple model for the effect of electronic noise that introduces a poor resolution of the photon number detected.
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In this paper, we introduce the motivation for Bell inequalities and give some background on two different types: CHSH and Mermin's inequalities. We present a proof for each and then show that certain quantum states can violate both of these inequalities. We introduce a new result stating that for four given measurement directions of spin, two respectively from Alice and two from Bob, which are able to produce a violation of the Bell inequality for an arbitrary shared quantum state will also violate the Bell inequality for a maximally entangled state. Then we provide another new result that characterizes all of the two-qubit states that violate Mermin's inequality.
We study Bell-inequality tests with entanglement between a coherent-state field in a cavity and a two-level atom. In order to detect the cavity field for such a test, photon on-off measurements and photon number parity measurements, respectively, are investigated. When photon on-off measurements are used, at least 50% of detection efficiency is required to demonstrate violation of the Bell inequality. Photon number parity measurements for the cavity field can be effectively performed using ancillary atoms and an atomic detector, which leads to large degrees of Bell violations up to Cirel'son's bound. We also analyze decoherence effects in both field and atomic modes and discuss conditions required to perform a Bell inequality test free from the locality loophole.
We develop a multimode theory of direct homodyne measurements of quantum optical quasidistribution functions. We demonstrate that unbalanced homodyning with appropriately shaped auxiliary coherent fields allows one to sample point-by-point different phase-space representations of the electromagnetic field. Our analysis includes practical factors that are likely to affect the outcome of a realistic experiment, such as nonunit detection efficiency, imperfect mode matching, and dark counts. We apply the developed theory to discuss feasibility of observing a loophole-free violation of Bell's inequalities by measuring joint two-mode quasidistribution functions by photon counting under locality conditions. We determine the range of parameters of the experimental setup that enable violation of Bell's inequalities for two states exhibiting entanglement in the Fock basis: a one-photon Fock state divided by a 50:50 beam splitter, and a two-mode squeezed vacuum state produced in the process of nondegenerate parametric down-conversion.