Quantum coherence as a signature of chaos

TL;DR

This paper establishes a rigorous link between quantum coherence and quantum chaos, demonstrating how coherence measures can diagnose chaos at the state and channel levels, supported by numerical and analytical results.

Contribution

It introduces coherence measures as diagnostic tools for quantum chaos, connecting them to chaos quantifiers and the out-of-time-ordered correlator, with both numerical and theoretical validation.

Findings

Quantum coherence measures relate closely to chaos quantifiers.

Numerical results show coherence of eigenstates aligns with random matrix theory.

The coherence-generating power is connected to the out-of-time-ordered correlator.

Abstract

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-vs-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 CGP-OTOC 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.