We propose two effective schemes for local and remote unknown atomic state comparisons with a cavity-assisted single photon input—output process without any initial entanglement or auxiliary resource. The unambiguous state discrimination is considered using the state comparison process as the basic module. All the implementation schemes here just involve common quantum logic gates and the single qubit measurement. The analysis shows that our schemes are feasible under the current experimental conditions.
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 $N\ensuremath{-}1$ copies of the data state are necessary for discriminating between
N unknown states of the combined system.
A universal programmable discriminator can perform discrimination between two unknown states, and the optimal solution can be approached via discrimination between the two averages over the uniformly distributed unknown input pure states, as has been widely discussed in previous works. In this paper, we consider the success probabilities of the optimal universal programmable unambiguous discriminators when applied to the pure input states. More precisely, the analytic results of the success probabilities are derived with the expressions of the optimal measurement operators for the universal discriminators, and we find that the success probabilities are independent of the dimension
d while the amount of copies in the two program registers is equal. The success probability of the programmable unambiguous discriminator can asymptotically approach that of the usual unambiguous discrimination (state comparison) as the number of copies in the program registers (data register) goes to infinity.