Optimal unambiguous state discrimination of two density matrices: A second class of exact solutions

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dc.creatorRaynal, Philippe
dc.creatorLütkenhaus, Norbert
dc.date2007-02-02
dc.date2007-11-03
dc.date.accessioned2026-07-07T08:48:26Z
dc.date.available2026-07-07T08:48:26Z
dc.descriptionWe consider the Unambiguous State Discrimination (USD) of two mixed quantum states. We study the rank and the spectrum of the elements of an optimal USD measurement. This naturally leads to a partial fourth reduction theorem. This theorem shows that either the failure probability equals its overall lower bound given in term of the fidelity or a two-dimensional subspace can be split off from the original Hilbert space. We then use this partial reduction theorem to derive the optimal solution for any two equally probable Geometrically Uniform (GU) states $ρ_0$ and $ρ_1=Uρ_0 U^\dagger$, $U^2={\openone}$, in a four-dimensional Hilbert space. This represents a second class of analytical solutions for USD problems that cannot be reduced to some pure state cases. We apply our result to answer two questions that are relevant in implementations of the Bennett and Brassard 1984 quantum key distribution protocol using weak coherent states.
dc.descriptionfinal published version: 18 pages, 5 figures. to appear in PRA
dc.identifierhttps://arxiv.org/abs/quant-ph/0702022
dc.identifierhttp://arxiv.org/abs/quant-ph/0702022
dc.identifierPhys. Rev. A Vol 76, 052322 (2007)
dc.identifierdoi:10.1103/PhysRevA.76.052322
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143949
dc.subjectQuantum Physics
dc.titleOptimal unambiguous state discrimination of two density matrices: A second class of exact solutions
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