Information gain in tomography - A quantum signature of chaos

TL;DR

This paper demonstrates that quantum chaos influences information gain in quantum tomography, with higher chaoticity leading to improved state reconstruction fidelity, supported by random matrix theory predictions.

Contribution

It introduces a method to detect quantum signatures of chaos through information gain metrics in quantum tomography, linking chaos to measurement efficiency.

Findings

Higher chaoticity correlates with increased information gain.

Fidelity of quantum state reconstruction improves with chaos.

Results align with predictions from random matrix theory.

Abstract

We find quantum signatures of classical chaos in various metrics of information gain in quantum tomography. We employ a quantum state estimator based on weak collective measurements of an ensemble of identically prepared systems. The tomographic measurement record consists of a sequence of expectation values of a Hermitian operator that evolves under repeated application of the Floquet map of the quantum kicked top. We find an increase in information gain and hence higher fidelities in the reconstruction algorithm when the chaoticity parameter map increases. The results are well predicted by random matrix theory.