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The discrimination between two unknown states can be performed by a universalprogrammable discriminator, where the copies of the two possible states arestored in two program systems respectively and the copies of data, which wewant to confirm, are provided in the data system. In the present paper, wepropose a group-theretic approach to the multi-copy programmable statediscrimination problem. By equivalence of unknown pure states to known mixedstates and with the representation theory of U(n) group, we construct theJordan basis to derive the analytical results for both the optimal unambiguousdiscrimination and minimum-error discrimination. The POVM operators forunambiguous discrimination and orthogonal measurement operators forminimum-error discrimination are obtained. We find that the optimal failureprobability and minimum-error probability for the discrimination between themean input mixd states are dependent on the dimension of the unknown quditstates. We applied the approach to generalize the results of He and Bergou(Phys. Rev. A {\bf 75}, 032316 (2007)) from qubit to qudit case, and we furthersolve the problem of programmable dicriminators with arbitrary copies ofunknown states in both program and data systems.

Group-theoretic approach for multi-copy programmable discriminators between two unknown qudit states