Typical dynamical quantum chaos probes are initial-state dependent (e.g., local observables or purities) and thus may fail to capture typical decoherent behavior one expects of a subsystem. Quantum channels fully capture the reduced dynamics of a subsystem. Here, we investigate the purity of the Choi state of a single spin in a chain, which acts as the state representation of the channel encoding the reduced dynamics. Operationally, we show this quantity functions as an echo protocol, termed the Choi echo. It measures the environment's recovery fidelity when subjected to a forward evolution, a completely depolarizing operation on the local subsystem, and a subsequent backward evolution. We investigate the equilibration value of the Choi echo across the integrability-to-chaos transition in three paradigmatic spin-$1/2$ chains. We show that average single-spin decoherence does not uniquely correspond to spectral chaos. Specifically, coherent transport in integrable systems can mimic the mean relaxation of a single spin typically induced by chaotic scrambling, generating false positives for spectral chaos. This work offers a perspective bridging quantum information tools with many-body quantum chaos.

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• Loschmidt echo
• Quantum channels
• Quantum chaos
• 1-dimensional spin chains
• Disordered systems
• Quantum many-body systems
• Heisenberg model
• Ising model