Choi echo: dynamical irreversibility and local decoherence in quantum many-body chaos

Quantifying intrinsic irreversibility in open quantum dynamics is central to understanding decoherence and information loss in many-body systems. In this work, we introduce the Choi echo, which provides an operational interpretation of the purity of the Choi state, the state representation of a quantum channel, as a quantifier of the robustness of quantum correlations against local information erasure. We employ this framework to analyze the reduced dynamics of a subsystem and to test whether local decoherence probes quantum chaos in many-body systems. Across paradigmatic spin chain models, we show that while the Choi echo captures key dynamical features, it also exhibits intrinsic limitations that, in certain regions of parameter space, restrict its ability to resolve the integrable-to-chaos transition at the level of spectral correlations. In particular, we demonstrate that local decoherence can spuriously signal quantum chaos in integrable regimes, tracing them to the inability of a strictly local probe to distinguish efficient coherent transport from genuinely scrambling dynamics. Our results show that local decoherence signals are controlled by the entanglement generated between the probe and its environment during the dynamics, rather than by spectral correlations, clarifying the practical scope of local dynamical diagnostics.