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Optimal unambiguous state discrimination of two density matrices: Lower bound and class of exact solutions

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Lutkenhaus,  N
Max Planck Research Group, Max Planck Institute for the Science of Light, Max Planck Society;

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Raynal, P., & Lutkenhaus, N. (2005). Optimal unambiguous state discrimination of two density matrices: Lower bound and class of exact solutions. PHYSICAL REVIEW A, 72(2): 022342. doi:10.1103/PhysRevA.72.022342.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002D-6DC8-E
Abstract
Recently the problem of unambiguous state discrimination of mixed quantum states has attracted much attention. So far, bounds on the optimum success probability have been derived [T. Rudolph, R. W. Spekkens, and P. S. Turner, Phys. Rev. A 68, 010301(R) (2003)]. For two mixed states they are given in terms of the fidelity. Here we give tighter bounds as well as necessary and sufficient conditions for two mixed states to reach these bounds. Moreover we construct the corresponding optimal measurement strategies. With this result, we provide analytical solutions for unambiguous discrimination of a class of generic mixed states. This goes beyond known results which are all reducible to some pure state case. Additionally, we show that examples exist where the bounds cannot be reached.