Quantum Fisher Information Perspective on Sensing in Anti-PT Symmetric Systems

TL;DR

This paper analyzes the fundamental limits of sensing sensitivity in anti-PT symmetric systems using quantum Fisher information, providing analytical bounds and emphasizing the role of long-lived resonances for enhanced measurement precision.

Contribution

It introduces a quantum Fisher information framework to derive the Cramer-Rao bound for anti-PT symmetric systems, advancing understanding of their sensing capabilities.

Findings

Analytical expression for the quantum Cramer-Rao bound in anti-PT systems.

Identification of long-lived resonances as key to enhanced sensing.

Validation of the framework through an illustrative example.

Abstract

The efficient sensing of weak environmental perturbations via special degeneracies called exceptional points in non-Hermitian systems has gained enormous traction in the last few decades. However, in contrast to the extensive literature on parity-time (PT) symmetric systems, the exotic hallmarks of anti-PT symmetric systems are only beginning to be realized now. Very recently, a characteristic resonance of vanishing linewidth in anti-PT symmetric systems was shown to exhibit tremendous sensitivity to intrinsic nonlinearities. Given the primacy of sensing in non-Hermitian systems, in general, and the immense topicality of anti-PT symmetry, we investigate the statistical bound to the measurement sensitivity for any arbitrary perturbation in a dissipatively coupled, anti-PT symmetric system. Using the framework of quantum Fisher information and the long-time solution to the full master equation, we analytically compute the Cramer-Rao bound for the system properties like the detunings and the couplings. As an illustrative example of this formulation, we inspect and reaffirm the role of a long-lived resonance in dissipatively interacting systems for sensing applications. \end{abstract}