Heisenberg-Weyl observables generate a family of maps that specializes to generalized Pauli channels in prime dimensions, with a d=3 positivity condition that includes the reduction map.
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A study on Heisenberg-Weyl linear maps
Heisenberg-Weyl observables generate a family of maps that specializes to generalized Pauli channels in prime dimensions, with a d=3 positivity condition that includes the reduction map.