Complementarity in atomic and oscillator systems

TL;DR

This paper presents a unified information-theoretic framework for understanding the complementarity between number and phase in atomic and oscillator quantum systems, deriving an entropy-based uncertainty principle.

Contribution

It introduces a novel entropy excess measure and applies it to both finite and infinite-dimensional systems, unifying their treatment of number-phase complementarity.

Findings

Derived a lower bound on entropy excess as an uncertainty principle

Unified the treatment of atomic and oscillator systems

Provided a new information-theoretic interpretation of number-phase complementarity

Abstract

We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems. The relevant uncertainty principle is obtained as a lower bound on {\it entropy excess}, the difference between number entropy and phase knowledge, the latter defined as the relative entropy with respect to the uniform distribution.