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- Bell inequalities for continuous-variable measurements
- He, Q. Y.; Cavalcanti, E. G.; Reid, M. D.; Drummond, P. D.
- Tests of local hidden-variable theories using measurements with continuous-variable (CV) outcomes are developed, and a comparison of different methods is presented. As examples, we focus on multipartite entangled Greenberger-Horne-Zeilinger and cluster states. We suggest a physical process that produces the states proposed here, and investigate experiments both with and without binning of the continuous variable. In the former case, the Mermin-Klyshko inequalities can be used directly. For unbinned outcomes, the moment-based Cavalcanti-Foster-Reid-Drummond inequalities are extended to functional inequalities by consideration of arbitrary functions of the measurements at each site. By optimizing these functions, we obtain more robust violations of local hidden-variable theories than with either binning or moments. Recent inequalities based on the algebra of quaternions and octonions are compared with these methods. Since the prime advantage of CV experiments is to provide a route to highly efficient detection via homodyne measurements, we analyze the effect of noise and detection losses in both binned and unbinned cases. The CV moment inequalities with an optimal function have greater robustness to both loss and noise. This could permit a loophole-free test of Bell inequalities.
- Publication type
- Journal article
- Research centre
- Swinburne University of Technology. Faculty of Engineering and Industrial Sciences. Centre for Atom Optics and Ultrafast Spectroscopy
- Physical Review A: Atomic, Molecular, and Optical Physics, Vol. 81, no. 6 (Jun 2010), article no. 062106
- Publication year
- FOR Code(s)
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics; 0204 Condensed Matter Physics; 0205 Optical Physics
- Bell inequalities; Continuous-variable measurements
- American Physical Society
- Publisher URL
- Copyright © 2010 The American Physical Society. Published version of the paper reproduced here with the kind permission of the publisher for non-commercial purposes only.
- Additional information
- The authors acknowledge support from the Australian Research Council through a Discovery grant and the Australian Research Council Center of Excellence for Quantum-Atom Optics.
- Full text
- Peer reviewed