Physics – Quantum Physics
Scientific paper
2007-12-28
Phys. Rev. A 77, 042105 (2008)
Physics
Quantum Physics
8 pages, no figures, REVTeX; published version
Scientific paper
10.1103/PhysRevA.77.042105
We have determined numerically the maximum quantum violation of over 100 tight bipartite Bell inequalities with two-outcome measurements by each party on systems of up to four dimensional Hilbert spaces. We have found several cases, including the ones where each party has only four measurement choices, where two dimensional systems, i.e., qubits are not sufficient to achieve maximum violation. In a significant proportion of those cases when qubits are sufficient, one or both parties have to make trivial, degenerate 'measurements' in order to achieve maximum violation. The quantum state corresponding to the maximum violation in most cases is not the maximally entangled one. We also obtain the result, that bipartite quantum correlations can always be reproduced by measurements and states which require only real numbers if there is no restriction on the size of the local Hilbert spaces. Therefore, in order to achieve maximum quantum violation on any bipartite Bell inequality (with any number of settings and outcomes), there is no need to consider complex Hilbert spaces.
Pal Karoly F.
Vértesi Tamas
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