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Quantum Optics Journal of the European Optical Society Part B

Violations of Bell's inequalities in multiparticle states generated using parametric amplification

William J. Munro, M. D. Reid

Published Feb 1, 1994• 3 citations
Publisher

Abstract

We suggest a new set of experiments designed to generate mesoscopic states which show a violation of a Bell's inequality. Possible experiments using parametric amplification are analysed and the effects of inefficient and noisy detection are discussed.
DOI
10.1088/0954-8998/6/1/001

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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.
We show that correlated photon-number states predicted to violate a Bell's inequality of the Clauser-Horne-Shimony-Holt type might be generated from parametric amplification. The test is potentially one of macroscopic quantum mechanics in that violations are predicted for situations where a large number of photons are detected in a single detector at one time. The traditional amplifier and detectors allow violation only for regimes where the probability of generation of a macroscopic state is very small. We suggest that this probability may be dramatically improved with the use of squeezing and photon-number-state-preparation techniques.
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We explore the challenges posed by the violation of Bell-like inequalities by d -dimensional systems exposed to imperfect state-preparation and measurement settings. We address, in particular, the limit of high-dimensional systems, naturally arising when exploring the quantum-to-classical transition. We show that, although suitable Bell inequalities can be violated, in principle, for any dimension of given subsystems, it is in practice increasingly challenging to detect such violations, even if the system is prepared in a maximally entangled state. We characterize the effects of random perturbations on the state or on the measurement settings, also quantifying the efforts needed to certify the possible violations in case of complete ignorance on the system state at hand.