Frankfurt 2006 – scientific programme

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SYSA: Quantum state analysis and estimation

SYSA 2: Quantum state analysis and estimation II

SYSA 2.2: Invited Talk

Tuesday, March 14, 2006, 14:30–15:00, HVI

Discriminating mixed quantum states: General relations and applications — •Ulrike Herzog — Institut für Physik, Humboldt-Universität Berlin, Newtonstr. 15, 12489 Berlin

State discrimination with minimum error, on the one hand, and optimum unambiguous state discrimination, on the other hand, are two different optimized measurement strategies for distinguishing between given quantum states that occur with given prior probabilities. In the latter case the discrimination is error-free provided that the measurement succeeds, but inconclusive results, where the measurement fails, are admitted as well, and their probability is minimized.

We provide general inequalities for the minimum failure probability in a measurement for optimum unambiguous discrimination of two mixed states, as well as exact solutions in certain special cases. Moreover, we discuss two applications for optimized mixed-state discrimination. The first is quantum state comparison, where we want to decide whether two quantum systems are in the same or different pure states, both of which are unknown and have arbitrary prior probabilities to occur. The second application is quantum state identification, where we assume that two reference qubits are prepared in two different but unknown pure states and that the state of a third qubit is guaranteed to coincide, with given prior probability of occurrence, with either one of these two states. We determine the two different optimized measurement strategies for identifying the state of the third qubit, studying also the modified problem that the state of one of the reference qubits is known.