Multicopy programmable discriminators between two unknown qudit states with group-theoretic approach

The discrimination between two unknown states can be performed by a universal programmable discriminator, where the copies of the two possible states are stored in two program systems respectively and the copies of data, which we want to confirm, are provided in the data system. In the present paper, we propose a group-theretic approach to the multi-copy programmable state discrimination problem. By equivalence of unknown pure states to known mixed states and with the representation theory of $U(n)$ group, we construct the Jordan basis to derive the analytical results for both the optimal unambiguous discrimination and minimum-error discrimination. The POVM operators for unambiguous discrimination and orthogonal measurement operators for minimum-error discrimination are obtained. We find that the optimal failure probability and minimum-error probability for the discrimination between the mean input mixd states are dependent on the dimension of the unknown qudit states. We applied the approach to generalize the results of He and Bergou (2007) from qubit to qudit case, and we further solve the problem of programmable dicriminators with arbitrary copies of unknown states in both program and data systems.

QUANTUM CIRCUITS FOR SINGLE-QUBIT MEASUREMENTS CORRESPONDING TO PLATONIC SOLIDS

Each platonic solid defines a single-qubit positive operator-valued measure (POVM) by interpreting its vertices as points on the Bloch sphere. We construct simple circuits for implementing these kinds of measurements and other simple types of symmetric POVMs on one qubit. Each implementation consists of a discrete Fourier transform and some elementary quantum operations followed by an orthogonal measurement in the computational basis.

Self testing quantum apparatus

We study, in the context of quantum information and quantum communication, a configuration of devices that includes (1) a source of some unknown bipartite quantum state that is claimed to be the Bell state $\Phi^+$ and (2) two spatially separated but otherwise unknown measurement apparatus, one on each side, that are each claimed to execute an orthogonal measurement at an angle $\theta \in \{-\pi/8, 0, \pi/8\}$ that is chosen by the user. We show that, if the nine distinct probability distributions that are generated by the self checking configuration, one for each pair of angles, are consistent with the specifications, the source and the two measurement apparatus are guaranteed to be identical to the claimed specifications up to a local change of basis on each side. We discuss the connection with quantum cryptography. testing quantum apparatus (pp273-286) D. Mayers and A. Yao We study, in the context of quantum information and quantum communication, a configuration of devices that includes (1) a source of some unknown bipartite quantum state that is claimed to be the Bell state $\Phi^+$ and (2) two spatially separated but otherwise unknown measurement apparatus, one on each side, that are each claimed to execute an orthogonal measurement at an angle $\theta \in \{-\pi/8, 0, \pi/8\}$ that is chosen by the user. We show that, if the nine distinct probability distributions that are generated by the self checking configuration, one for each pair of angles, are consistent with the specifications, the source and the two measurement apparatus are guaranteed to be identical to the claimed specifications up to a local change of basis on each side. We discuss the connection with quantum cryptography.

SCHEMES FOR REMOTELY PREPARING MULTIPARTITE EQUATORIAL ENTANGLED STATES IN HIGH DIMENSIONS

In this paper, we present two kinds of schemes for remotely preparing multiparticle d-dimensional equatorial entangled states with unit probability. It is found that the first remote state preparation scheme is realized by a multiparticle projective measurement, while the second scheme is achieved by a single particle orthogonal measurement. Each scheme can be perfectly implemented whatsoever the particle number N and the dimension d are.