Success Probability Of Discrimination Research Articles

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

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 ${N}_{D}$ 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 $N\ensuremath{-}1$ copies of the data state are necessary for discriminating between $N$ unknown states of the combined system.

远程协作实现对线性相关对称高维量子态的最大信心辨识

Based on nonlocal two-level controlled-rotation gates, the maximum-confident discrimination among <italic>N</italic> linearly dependent symmetric <italic>d</italic>-level quantum states implemented by two remote parters could be realized (<italic>N</italic>&gt;<italic>d</italic>). We present a scheme for such kind of nonlocal maximum-confident quantum state discrimination. In this scheme, the sequential nonlocal positive operator valued measurements (POVMs) lies at the heart. We construct the required optimal POVMs, in which each POVM has only two remote detection operators. We also report on the quantitative relations between the success probability of discrimination, entanglement and classical communication resources required in the implementation. The fact that the two-outcome nonlocal 2<italic>m</italic>×2<italic>m</italic> POVM could be realized using only (<italic>m</italic>-1) two-level maximally entangled pairs is notable. This scheme is feasible for current experimental technology.

Quantum state separation, unambiguous discrimination and exact cloning

Unambiguous discrimination and exact cloning reduce the square-overlap between quantum states, exemplifying the more general type of procedure we term state separation. We obtain the maximum probability with which two equiprobable quantum states can be separated by an arbitrary degree, and find that the established bounds on the success probabilities for discrimination and cloning are special cases of this general bound. The latter also gives the maximum probability of successfully producing N exact copies of a quantum system whose state is chosen secretly from a known pair, given M initial realizations of the state, where N > M. We also discuss the relationship between this bound and that on unambiguous state discrimination.