Uncertainty Relation for Non-Hermitian Systems

TL;DR

This paper develops an uncertainty relation for finite-dimensional PT-invariant non-Hermitian quantum systems, demonstrating enhanced quantum Fisher information gain and potential for advanced quantum sensing near exceptional points.

Contribution

It introduces a new uncertainty relation framework for non-Hermitian systems using good observables, highlighting improved measurement precision over Hermitian systems.

Findings

Enhanced quantum Fisher information in non-Hermitian systems

Minimum uncertainty states near exceptional points

Potential for non-Hermitian quantum sensors

Abstract

We construct uncertainty relation for arbitrary finite dimensional PT invariant non-Hermitian quantum systems within a special inner product framework. This construction is led by good observables which are a more general class of operators. We show that the cumulative gain in the quantum Fisher information when measuring two good observables for such non-Hermitian systems is way better than their Hermitian counterpart. Minimum uncertainty states being the best candidates for this gain near the exceptional point supports the intelligent or simultaneous non-Hermitian quantum sensors.