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arXiv:quant-ph/0006057 · Physical Review Letters

Proposal for the Measurement of Bell-Type Correlations from Continuous Variables

Timothy C. Ralph, William J. Munro, Rodney Polkinghorne

Published Sep 4, 2000• 54 citations
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Abstract

We show theoretically that Bell-type correlations can be observed between continuous variable measurements performed on a parametric source. An auxiliary measurement, performed on the detection environment, negates the possibility of constructing a local realistic description of these correlations.
DOI
10.1103/physrevlett.85.2035

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Konrad Banaszek, Ian A. Walmsley, K. Wódkiewicz

In a recent paper [T. C. Ralph, W. J. Munro, R. E. S. Polkinghorne, Phys. Rev. Lett. 85, 2035 (2000)], the authors propose a test for Bell's inequalities based on quadrature measurements for a correlated parametric source. We present here a local hidden variable model which reproduces all the expectation values predicted in the described experimental scheme, and point out that the proposal is based on an inconsistent use of Bell's inequalities.

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Reply to Comment on ``Proposal for the Measurement of Bell-Type Correlations from Continuous Variables''

Timothy C. Ralph, William J. Munro

Recently K. Banaszek, I. A. Walmsley, K. Wodkiewicz (quant-ph/0012097) commented on our Proposal for the Measurement of Bell-Type Correlations from Continuous Variables [T. C. Ralph, W. J. Munro, R. E. S. Polkinghorne, Phys. Rev. Lett. 85, 2035 (2000)]. Their comment is based on a blatant misreading and misunderstanding of our letter and as such is simply wrong.

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We have theoretically investigated the possibility of using any of several continuous-variable Bell-type inequalities---for which the dichotomic measurements are achieved with coarse-grained quadrature (homodyne) measurements---in a multiparty configuration where each participant is given a section, in the frequency domain, of the output of an optical parametric oscillator which has been synchronously pumped with a frequency comb. Such light sources are undergoing intense study due to their novel properties, including the potential for production of light entangled in many hundreds of physical modes---a critical component for many proposals in optical or hybrid-optical quantum computation proposals. The situation we study notably uses only highly efficient optical homodyne detection, meaning that in such systems the fair-sampling loophole would be relatively easy to avoid.
Over the past three decades, numerous demonstrations of the violation of Bell’s inequalities have been reported in optical experiments based upon observations of polarization correlations for photon pairs. Without exception, these measurements as well as those in other systems have involved discrete variables for which the Bell inequalities are applicable. By contrast, an experiment to demonstrate the original proposal by Einstein, Podolsky, and Rosen (EPR)1 for a system of observables with a continuous spectrum has not previously been realized. From many possible theoretical avenues, we have followed the suggestion of Reid and Drummond2 to achieve a demonstration of the EPR paradox for continuous variables by employing a subthreshold optical parametric oscillator (OPO) operated in a frequency-degenerate but polarization-nondegenerate mode.