Frankfurt 2006 – scientific programme
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Q: Quantenoptik und Photonik
Q 63: Quanteninformation V
Q 63.8: Talk
Thursday, March 16, 2006, 15:45–16:00, HVI
Optimal unambiguous state discrimination of two density matrices — •philippe raynal and Norbert Luetkenhaus — Institut für theoretische Physik I, Max-Planck-Forschungsgruppe, Universität Erlangen-Nürnberg, Staudtstr. 7/B1, 91058 Erlangen
Quantum state discrimination is a fundamental task in quantum information theory. The signals are usually nonorthogonal quantum states, which implies that they can not be perfectly distinguished. One possible discrimination strategy is the so-called Unambiguous State Discrimination where the states are successfully identified only with some probability, but without error. The optimal USD measurement has been extensively studied for pure states, especially for any pair of pure states. In the case of a pair of generic mixed states, no complete solution is known. However, the dimension of the generic problem can often be reduced [1]. Moreover bounds on the optimal success probability have been derived [2,3] and for a given pair of mixed states those bounds can be reached if and only if two explicit conditions are met [3]. We go beyond this result by providing optimal solutions for any two states ρ0 and ρ1=U ρ0 U, U2=1 in dimension 4 with equal a priori probabilities. ρ0 and ρ1 are called Geometrically Uniformed states. This class of problems includes the discrimination of the basis information in the BB84 QKD protocol with coherent states.
[1] Ph. Raynal, N. Lütkenhaus, S.J. van Enk, PRA 68, 022308 (2003)
[2] Ph. Raynal, N. Lütkenhaus, PRA 72, 022342 (2005)
[3] U. Herzog, PRA 71, 042314 (2005)