Characterizing and Quantifying Quantum Chaos with Quantum Tomography

TL;DR

This paper investigates how quantum chaos influences the rate of information gain in quantum tomography, revealing that chaoticity and symmetry class affect state reconstruction fidelity, with results supported by random matrix theory.

Contribution

It introduces a novel approach linking quantum chaos signatures to quantum tomography performance, providing analytical bounds and predictions for information gain based on symmetry and chaoticity.

Findings

Information gain increases with chaoticity of the quantum map.

Symmetry class affects the rate of information gain.

Random matrix theory accurately describes the fully chaotic regime.

Abstract

We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under application of the Floquet operator of a quantum map that possesses (or lacks) time reversal symmetry. We find that the rate of information gain, and hence the fidelity of quantum state reconstruction, depends on the symmetry class of the quantum map involved. Moreover, we find an increase in information gain and hence higher reconstruction fidelities when the Floquet maps employed increase in chaoticity. We make predictions for the information gain and show that these results are well described by random matrix theory in the fully chaotic regime. We derive analytical expressions for bounds on information gain using random matrix theory for different class of maps and show that these bounds are realized by fully chaotic quantum systems.