Operator formalism for the Wigner phase distribution

Abstract

We construct a Hermitian phase operator for the radially integrated Wigner distribution, which is known to be sensitive to phase. We show that this operator is complete and also elucidate a set of complete but non-orthogonal states that seems to be naturally associated with such an operator. Further, we show that our operator satisfies a weak equivalence relation with the Pegg–Barnett operator, thus showing that the essential phase information furnished by both formalisms are the same. It is also shown that this operator gives results which are in agreement with the expected uniform phase distribution of a Fock state.