Physics – Quantum Physics
Scientific paper
2007-02-02
Phys. Rev. A Vol 76, 052322 (2007)
Physics
Quantum Physics
final published version: 18 pages, 5 figures. to appear in PRA
Scientific paper
10.1103/PhysRevA.76.052322
We 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 $\rho_0$ and $\rho_1=U\rho_0 U^\dagger$, $U^2={\openone}$, 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.
Lütkenhaus Norbert
Raynal Philippe
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