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 \textit{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.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 \textit{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.

quant-pharXiv:2512.11030Physical Review ADec 15, 20250 citations

Quantum theory of channeling

Yu. A. Kashlev

Theoretical and Mathematical PhysicsApr 1, 19813 citations

Topological Properties of Quantum Information Channels (Mathematical Aspects of Quantum Information and Quantum Chaos)

Shigeo Akashi

Apr 1, 20000 citations

Quantum coherence as a signature of chaos

Namit Anand, Georgios Styliaris, Meenu Kumari +1 more

We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos.We quantify this connection at two different levels: quantum states and quantum channels.At the level of states, we show how several well-studied quantifiers of chaos are, in fact, quantum coherence measures in disguise (or closely related to them).We further this connection for all quantum coherence measures by using tools from majorization theory.Then we numerically study the coherence of chaotic-versus-integrable eigenstates and find excellent agreement with random matrix theory in the bulk of the spectrum.At the level of channels, we show that the coherence-generating power (CGP)-a measure of how much coherence a dynamical process generates on average-emerges as a subpart of the out-of-time-ordered correlator (OTOC), a measure of information scrambling in many-body systems.Via numerical simulations of the (nonintegrable) transverse-field Ising model, we show that the OTOC and CGP capture quantum recurrences in quantitatively the same way.Moreover, using random matrix theory, we analytically characterize the OTOC-CGP connection for the Haar and Gaussian ensembles.In closing, we remark on how our coherence-based signatures of chaos relate to other diagnostics, namely, the Loschmidt echo, OTOC, and the Spectral Form Factor.We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos.We quantify this connection at two different levels: quantum states and quantum channels.At the level of states, we show how several well-studied quantifiers of chaos are, in fact, quantum coherence measures in disguise (or closely related to them).We further this connection for all quantum coherence measures by using tools from majorization theory.Then we numerically study the coherence of chaotic-versus-integrable eigenstates and find excellent agreement with random matrix theory in the bulk of the spectrum.At the level of channels, we show that the coherence-generating power (CGP)-a measure of how much coherence a dynamical process generates on average-emerges as a subpart of the out-of-time-ordered correlator (OTOC), a measure of information scrambling in many-body systems.Via numerical simulations of the (nonintegrable) transverse-field Ising model, we show that the OTOC and CGP capture quantum recurrences in quantitatively the same way.Moreover, using random matrix theory, we analytically characterize the OTOC-CGP connection for the Haar and Gaussian ensembles.In closing, we remark on how our coherence-based signatures of chaos relate to other diagnostics, namely, the Loschmidt echo, OTOC, and the Spectral Form Factor.

arXiv:2009.02760Physical Review ResearchJun 17, 202149 citations

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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.