Implementation of group-covariant positive operator valued measures by orthogonal measurements

摘要: We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark’s theorem POVM can be implemented by an orthogonal measurement larger Accordingly, our goal is to find circuit implementation of given which uses the symmetry POVM. Based representation theory group we develop general approach for POVMs consist rank-one operators. The construction relies method decompose matrices that intertwine two representations group. give several examples resulting circuits are efficient. In particular, obtain efficient class generated Weyl–Heisenberg groups. These allow implement approximative simultaneous position and crystal momentum particle moving cyclic chain.