Uncertainty Relation for Non-Hermitian Systems

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.

9 pages, 5 figures

References in corpus (6)

• Making Sense of Non-Hermitian Hamiltonians
• Stronger uncertainty relations for the sum of variances
• Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
• Quantum Fisher information from randomized measurements
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• A chain of solvable non-Hermitian Hamiltonians constructed by a series of metric operators

Cited by in corpus (8)

• Non-Hermitian Stark Many-Body Localization
• PT-Symmetry Breaking Transitions in Polymeric Systems
• One-dimensional L{é}vy Quasicrystal
• A Hermitian bypass to the non-Hermitian quantum theory
• Stronger sum uncertainty relations for non-Hermitian operators
• Uncertainty Relation for Pseudo-Hermitian Quantum Systems
• Emergence of Hermitian topology from non-Hermitian knots
• Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model