Maximal violation of a bipartite three-setting, two-outcome Bell inequality using infinite-dimensional quantum systems
- Institute of Nuclear Research of the Hungarian Academy of Sciences, Post Office Box 51, H-4001 Debrecen (Hungary)
The I{sub 3322} inequality is the simplest bipartite two-outcome Bell inequality beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In the case of the CHSH inequality the maximal quantum violation can already be attained with local two-dimensional quantum systems; however, there is no such evidence for the I{sub 3322} inequality. In this paper a family of measurement operators and states is given which enables us to attain the maximum quantum value in an infinite-dimensional Hilbert space. Further, it is conjectured that our construction is optimal in the sense that measuring finite-dimensional quantum systems is not enough to achieve the true quantum maximum. We also describe an efficient iterative algorithm for computing quantum maximum of an arbitrary two-outcome Bell inequality in any given Hilbert space dimension. This algorithm played a key role in obtaining our results for the I{sub 3322} inequality, and we also applied it to improve on our previous results concerning the maximum quantum violation of several bipartite two-outcome Bell inequalities with up to five settings per party.
- OSTI ID:
- 21448443
- Journal Information:
- Physical Review. A, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevA.82.022116; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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