Formal relation between Pegg-Barnett and Paul quantum phase frameworks

TL;DR

This paper establishes a precise mathematical link between two major quantum phase formalisms, showing that the Paul approach can be derived from the Pegg-Barnett method using a quantum amplifier, thus unifying different perspectives.

Contribution

It explicitly connects the Pegg-Barnett and Paul quantum phase frameworks, revealing that the Paul formalism emerges as a semi-classical limit of the Pegg-Barnett approach.

Findings

The probability distribution in the Paul formalism is derived from Pegg-Barnett using an amplifier channel.

The Paul framework can be interpreted as a semi-classical limit of the Pegg-Barnett formalism.

The work provides a unified view of quantum phase formalisms.

Abstract

The problem of defining a hermitian quantum phase operator is nearly as old as quantum mechanics itself. Throughout the years, a number of solutions was proposed, ranging from abstract operator formalisms to phase-space methods. In this work, we make an explicit connection between two of the most prominent approaches, by proving that the probability distribution of phase in the Paul formalism follows exactly from the Pegg-Barnett formalism by combining the latter with the quantum limited amplifier channel. Our findings suggest that the Paul framework may be viewed as a semi-classical limit of the Pegg-Barnett approach.