Effect of chaos on information gain in quantum tomography

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.

11 pages, 6 figures, published version with modified title

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Cited by in corpus (5)

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• Quantifying operator spreading and chaos in Krylov subspaces with quantum state reconstruction
• Unravelling quantum chaos using persistent homology
• Loschmidt echo and scrambling of systematic errors in tomography -- a quantum signature of chaos
• Information acquisition, scrambling, and sensitivity to errors in quantum chaos