Effect of chaos on information gain in quantum tomography

TL;DR

This paper investigates how chaos in quantum dynamics affects information gain in quantum tomography, revealing that chaos can hinder or help state reconstruction depending on the state type and their alignment with operator spreading.

Contribution

It provides a detailed analysis of the impact of chaos on quantum tomography fidelity, highlighting the importance of state type and operator alignment in information gain.

Findings

Chaos decreases fidelity for spin coherent states.

Chaos can enhance information gain for random states.

Operator spreading's role is crucial for tomography success.

Abstract

Does chaos in the dynamics enable information gain in quantum tomography or impede it? We address this question by considering continuous measurement tomography in which the measurement record is obtained as a sequence of expectation values of a Hermitian observable evolving under the repeated application of the Floquet map of the quantum kicked top. For a given dynamics and Hermitian observables, we observe completely opposite behavior in the tomography of well-localized spin coherent states compared to random states. As the chaos in the dynamics increases, the reconstruction fidelity of spin coherent states decreases. This contrasts with the previous results connecting information gain in tomography of random states with the degree of chaos in the dynamics that drives the system. The rate of information gain and hence the fidelity obtained in tomography depends not only on the degree of chaos in the dynamics and to what extent it causes the initial observable to spread in various directions of the operator space but, more importantly, how well these directions are aligned with the density matrix to be estimated. Our study also gives an operational interpretation for operator spreading in terms of fidelity gain in an actual quantum information tomography protocol.