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

Journal Article · Thu Nov 15 04:00:00 EST 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.76.052322· OSTI ID:21027984

Raynal, Philippe; Luetkenhaus, Norbert ^[1]

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1. Quantum Information Theory Group, Institut fuer Theoretische Physik I, and Max-Plank-Forschungsgruppe, Institut fuer Optik, Information und Photonik Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen (Germany)

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 terms 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 states {rho}{sub 0} and {rho}{sub 1}=U{rho}{sub 0}U{sup {dagger}}, U{sup 2}=1, 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.

• OSTI ID: 21027984
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 76; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
DENSITY MATRIX
DISTRIBUTION
EIGENSTATES
EXACT SOLUTIONS
FOUR-DIMENSIONAL CALCULATIONS
HILBERT SPACE
QUANTUM CRYPTOGRAPHY
REDUCTION
SPECTRA
TWO-DIMENSIONAL CALCULATIONS