Quantum timekeeping and the dynamics of scrambling in critical systems

• URL: http://arxiv.org/abs/2603.13016v1
• Date: Fri, 13 Mar 2026 14:21:49 GMT
• Title: Quantum timekeeping and the dynamics of scrambling in critical systems
• Abstract summary: We show that local subsystems of information scrambling systems naturally function as quantum stopwatches.<n>Treating time as the estimation parameter, we derive a generalized quantum Cramer-Rao bound.<n>Using a scaling analysis based on imaginary-time correlators, we show that the subsystem QFI exhibits universal critical amplification near quantum phase transitions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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