Quantum timekeeping and the dynamics of scrambling in critical systems

TL;DR

This paper introduces a quantum metrological approach to quantum chaos, linking subsystem quantum Fisher information and out-of-time correlators to time estimation and critical phenomena.

Contribution

It develops a framework connecting quantum chaos, time estimation, and criticality using subsystem quantum Fisher information and out-of-time correlators.

Findings

Subsystem QFI encodes passage of time in scrambling systems.

Derived a quantum Cramer-Rao bound relating time estimation precision to OTOCs and QFI.

Subsystem QFI shows universal critical amplification near quantum phase transitions.

Abstract

In this work, we develop a quantum metrological framework for quantum chaos by showing that local subsystems of information scrambling systems naturally function as quantum stopwatches. The reduced quantum state of a subsystem encodes the passage of time through its growing distinguishability from the initial preparation. Treating time as the estimation parameter, we then derive a generalized quantum Cramer-Rao bound that directly relates the precision of time estimation to the decay of out-of-time ordered correlators (OTOCs) and subsystem quantum Fisher information (QFI). As a main result, we obtain continuity bounds for quantum Lyapunov exponent in terms of the subsystem QFI in quantumly chaotic dynamics. Furthermore, using a scaling analysis based on imaginary-time correlators, we show that the subsystem QFI exhibits universal critical amplification near quantum phase transitions. Our results are demonstrated and verified by a numerical analysis of the dynamics of a chaotic Ising chain.