Translations and reflections on the torus: identities for discrete Wigner functions and transforms

A finite Hilbert space can be associated to a periodic phase space, that is, a torus. Then a
subgroup of operators corresponding to reflections and translations on the torus form respectively
the basis for the discrete Weyl representation, including the Wigner function, and for its Fourier
conjugate, the chord representation. They are invariant under Clifford transformations and obey
analogous product rules to the continuous representations, so allowing for the calculation of
expectations and correlations for observables. We here import new identities from the continuum for
products of pure state Wigner and chord functions, involving, for instance the inverse phase space
participation ratio and correlations of a state with its translate. New identities are derived
involving transition Wigner or chord functions of transition operators ##IMG##
[] . Extension of the reflection
and transl...

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