Designing an optimal, universal, programmable, and unambiguous discriminator for N unknown qubits

摘要

The universal programmable discriminator is a device for discrimination between unknown quantum states. It has two kinds of registers: the program register and the data register. The states that are stored in registers are all unknown. It is assured that the data state is identical with one of the program states with the certain probability. The aim is to optimally identify the state stored in the data register with one of the program states that it is done by discriminating between unknown states of the combined system contains program and data registers.We design an optimal universal unambiguous programmable discriminator that has N qubit systems in the program register, to unambiguously identify the qubit state of data with one of N program qubit states. All unknown qubit states are pure and ND copies of the data state are available. We determine the optimal positive-operator valued measure (POVM) elements in two different ways. First, we find optimal POVMs that maximize the average of the overall success probability of discrimination between N unknown pure states of the combined system. In another way, the problem of discrimination between N unknown pure states of the combined system is reduced to discrimination between N known average mixed states. It is shown that theses two different ways lead to the same results. We show that at least N - 1 copies of the data state are necessary for discriminating between N unknown states of the combined system.