By Decker T., Janzing D.
We contemplate group-covariant optimistic operator valued measures (POVMs) on afinite dimensional quantum approach. Following Neumark's theorem a POVM can beimplemented via an orthogonal dimension on a bigger method. as a result, ourgoal is to discover a quantum circuit implementation of a given group-covariant POVMwhich makes use of the symmetry of the POVM. according to illustration idea of thesymmetry workforce we enhance a normal procedure for the implementation of groupcovariantPOVMs which include rank-one operators. the development will depend on amethod to decompose matrices that intertwine representations of a finite group.We provide a number of examples for which the ensuing quantum circuits are effective. Inparticular, we receive effective quantum circuits for a category of POVMs generated byWeyl-Heisenberg teams. those circuits let to enforce an approximative simultaneousmeasurement of the location and crystal momentum of a particle movingon a cyclic chain.
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