Correlated Entropic Uncertainty as a Signature of Exceptional Points

TL;DR

This paper reveals that the behavior of eigenfunctions near exceptional points in non-Hermitian systems is governed by a fundamental entropic uncertainty trade-off, linking phase entropy and Fourier entropy, and establishing biorthogonality as an intrinsic property.

Contribution

It introduces a universal entropic uncertainty framework explaining eigenfunction behavior at exceptional points, advancing the fundamental understanding of non-Hermitian physics.

Findings

Entropic trade-off governs eigenfunction behavior near exceptional points

Biorthogonality is an intrinsic property, not an anomaly

Framework can be tested with interferometric techniques

Abstract

Non-Hermitian physics has become a fundamental framework for understanding open systems where gain and loss play essential roles, with impact across photonics, quantum science, and condensed matter. While the role of complex eigenvalues is well established, the nature of the corresponding eigenfunctions has remained a long-standing problem. Here we show that it arises from a fundamental entropic uncertainty trade-off between phase entropy and its Fourier representation. This trade-off enforces a correlated behavior of phase and Fourier entropies near avoided crossings and exceptional points, precisely where the Petermann factor diverges and phase rigidity collapses. Our results establish biorthogonality is not as an anomaly but an intrinsic property of eigenfunctions, arising universal manifestation of uncertainty relation in non-Hermitian systems. Beyond resolving this foundational question, our framework provides a unifying and testable principle that advances the fundamentals of non-Hermitian physics and can be directly verified with existing interferometric techniques.