On some properties of number-phase Wigner function

TL;DR

This paper demonstrates that the number-phase Wigner function uniquely determines the density operator and explores its relation to Glauber-Sudarshan and Cahill-Glauber distributions, extending the understanding of quantum phase space representations.

Contribution

It establishes the unique correspondence between the number-phase Wigner function and the density operator, and generalizes the relation to Cahill-Glauber distributions.

Findings

Number-phase Wigner function uniquely determines the density operator.

Relations between Wigner function and Glauber-Sudarshan distribution are derived.

Generalization to Cahill-Glauber distributions is achieved.

Abstract

It is shown that the number-phase Wigner function defines uniquely the respective density operator. Relations between the Glauber-Sudarshan distribution $\mathcal{P}(\alpha)$ and the number-phase Wigner function is found. This result is then generalised to the case of the Cahil-Glauber distributions $\mathcal{W}^{(s)}(\alpha)$, $-1\leq s \leq 1$.