We propose an experimental setup for discriminating four linearly independent nonorthogonal symmetric quantum states. The setup is based on linear optics only and can be configured to implement both optimal unambiguous state discrimination [Chefles and Barnett, Phys. Lett. A 250, 223 (1998)] and minimum error discrimination. In both cases, the setup is characterized by an optimal success probability. The experimental setup can be generalized to the case of discrimination among
N linearly nonorthogonal symmetric quantum states. We also study the discrimination between two incoherent superpositions of symmetric states. In this case, the setup also achieves an optimal success probability in the case of unambiguous discrimination as well as minimum error discrimination.
Quantum state discrimination is a fundamental task having many applications in quantum information processing. However up to now there has been no rigorous formulation for discriminating
N-qudit states. In this article we provide a geometric method to obtain minimum error discrimination for
N-qudit states. By using the geometric approach to minimum-error discrimination for
N-qudit states, we supply the condition for the existence of optimal measurement that can be composed of null operators, which gives a key understanding for discriminating
N-qudit states. Furthermore we present how the number of nonzero operators for optimal measurement can be reduced. Applying our method to symmetric
N-qudit states we obtain optimal measurements, which are different from known ones.
A set of linearly independent nonorthogonal symmetric d -level quantum states can be discriminated remotely and unambiguously with the aid of two-level Einstein–Podolsky–Rosen (EPR) states. We present a scheme for such a kind of remote unambiguous quantum state discrimination (UD). The probability of discrimination is in agreement with the optimal probability for local unambiguous discrimination among d symmetric states (Chefles and Barnettt 1998 Phys. Lett. A 250 223). This scheme consists of a remote generalized measurement described by a positive operator valued measurement (POVM). This remote POVM can be realized by performing a nonlocal 2 d × 2 d unitary operation on two spatially separated systems, one is the qudit which is encoded by one of the d symmetric nonorthogonal states to be distinguished and the other is an ancillary qubit, and a conventional local von Neumann orthogonal measurement on the ancilla. By decomposing the evolution process from the initial state to the final state, we construct a quantum network for realizing the remote POVM with a set of two-level nonlocal controlled-rotation gates, and thus provide a feasible physical means to realize the remote UD. A two-level nonlocal controlled-rotation gate can be implemented by using a two-level EPR pair in addition to local operations and classical communications (LOCCs).