Decomposition of the Brukner-Zeilinger invariant information with applications in wave-particle duality

School of Mathematics and Physics, University of Science and Technology Beijing - Beijing 100083, China

Received: 9 October 2025
Accepted: 28 November 2025

Abstract

In order to measure the inherent information content in a quantum state, Brukner and Zeilinger developed the idea of operationally invariant information in terms of the outcome probabilities of measuring a whole collection of mutually complementary observables. In this work, by partitioning the orthonormal operator basis of the associated operator Hilbert space into two complementary subsets, we establish a new decomposition of the Brukner-Zeilinger information. We further demonstrate that the two complementary components of the Brukner-Zeilinger information capture nicely the wave and particle features encoded in the quantum state after an n-path interferometer. Thus, we establish a universal complementarity relation involving the interference (wave feature) and the predictability (particle feature) via the unified concept of the Brukner-Zeilinger invariant information. These findings provide new characterizations of the wave-particle duality via the fundamental Brukner-Zeilinger invariant information.