A unified view of the discrimination problem of quantum states
State discrimination is a fundamental measurement primitive in quantum information processing. It is the key element in quantum key distribution, security analyses and probabilistic quantum algorithms. State discrimination deals with the following problem [1]: One is given a quantum system that was prepared in one of N known quantum states, but we don't know which. The task is to identify the state of the system as well as allowed by the laws of quantum mechanics. If the possible states are not mutually orthogonal the
problem is highly nontrivial and optimization with respect to some reasonable criteria leads to complex measurement strategies often involving generalized measurements. Finding the optimum measurement strategy is the subject of state discrimination.
The two fundamental discrimination strategies are the so‐called minimum-error (ME) strategy and the unambiguous discrimination (UD) strategy. In ME, every time a system is given and a measurement is performed on it a conclusion must be drawn about its state. Errors are permitted and in the optimal strategy the probability of making an error is
minimized. In UD, no errors are permitted but the price to pay is that an inconclusive measurement outcome must be permitted. When it occurs we don't learn anything about the state of the system and in the optimal strategy the probability of the inconclusive outcome is minimized.
There are two longstanding open problems associated with these strategies. One of them is to find the optimum UD strategy for the discrimination of more than two states. The other can be formulated as the following: UD and ME can be regarded as the two extremes of a more general strategy that continuously and optimally interpolates between them. The second open problem is to find this more general strategy. In this talk I’ll describe the solution to both of these longstanding open problems.
Event date: 24.01.2012, 14:00 to 24.01.2012, 16:00Speaker: Janos Bergou, Department of Physics and Astronomy Hunter College of the City University of New York, USA
Location: IQOQI, Seminarraum, 2nd Floor Boltzmanngasse 3, 1090 Vienna
