Phase-number uncertainty from Weyl commutation relations

TL;DR

This paper derives uncertainty relations for phase and number variables using Weyl commutation relations, highlighting contradictions in characteristic function combinations for finite and single-mode systems.

Contribution

It introduces new uncertainty relations for phase and number based on Weyl relations, applicable to finite-dimensional and single-mode quantum systems.

Findings

Uncertainty relations for phase and number are derived from Weyl commutation relations.

Contradictions between product and sum of characteristic functions are identified.

Applications include finite spin-like systems and single-mode field analysis.

Abstract

We derive suitable uncertainty relations for characteristics functions of phase and number variables obtained from the Weyl form of commutation relations. This is applied to finite-dimensional spin- like systems, which is the case when describing the phase difference between two field modes, as well as to the phase and number of a single-mode field. Some contradictions between the product and sums of characteristic functions are noted.