854 research outputs found
The geometric measure of entanglement for a symmetric pure state with positive amplitudes
In this paper for a class of symmetric multiparty pure states we consider a
conjecture related to the geometric measure of entanglement: 'for a symmetric
pure state, the closest product state in terms of the fidelity can be chosen as
a symmetric product state'. We show that this conjecture is true for symmetric
pure states whose amplitudes are all non-negative in a computational basis. The
more general conjecture is still open.Comment: Similar results have been obtained independently and with different
methods by T-C. Wei and S. Severini, see arXiv:0905.0012v
The chain rule implies Tsirelson's bound: an approach from generalized mutual information
In order to analyze an information theoretical derivation of Tsirelson's
bound based on information causality, we introduce a generalized mutual
information (GMI), defined as the optimal coding rate of a channel with
classical inputs and general probabilistic outputs. In the case where the
outputs are quantum, the GMI coincides with the quantum mutual information. In
general, the GMI does not necessarily satisfy the chain rule. We prove that
Tsirelson's bound can be derived by imposing the chain rule on the GMI. We
formulate a principle, which we call the no-supersignalling condition, which
states that the assistance of nonlocal correlations does not increase the
capability of classical communication. We prove that this condition is
equivalent to the no-signalling condition. As a result, we show that
Tsirelson's bound is implied by the nonpositivity of the quantitative
difference between information causality and no-supersignalling.Comment: 23 pages, 8 figures, Added Section 2 and Appendix B, result
unchanged, Added reference
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