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.

arXiv comment11 pages, 6 figures, published version with modified title

References in corpus (34)

• A bound on chaos
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• Direct Measurement of the Quantum Wavefunction
• Measuring the scrambling of quantum information
• Ergodic dynamics and thermalization in an isolated quantum system
• Out-of-time-order correlators in quantum mechanics
• Quantum Tomography
• Entanglement as a signature of quantum chaos
• Weak Quantum Chaos
• Testing statistical bounds on entanglement using quantum chaos
• Entangling power of quantized chaotic systems
• Continuous Weak Measurement and Nonlinear Dynamics in a Cold Spin Ensemble
• Quantum Tomography Protocols with Positivity are Compressed Sensing Protocols
• State tomography via weak measurements
• Efficient Quantum State Estimation by Continuous Weak Measurement and Dynamical Control
• Information-theoretic characterization of quantum chaos
• Quantum state reconstruction via continuous measurement
• Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos
• Complete characterization of post-selected quantum statistics using weak measurement tomography
• Quantum ergodicity and entanglement in kicked coupled-tops
• Quantum Chaos and the Correspondence Principle
• Informational completeness in bounded-rank quantum-state tomography
• The power of being positive: Robust state estimation made possible by quantum mechanics
• Strictly-complete measurements for bounded-rank quantum-state tomography
• Signatures of chaos in the dynamics of quantum discord
• Invariant information and quantum state estimation
• Random unitary maps for quantum state reconstruction
• Information gain in tomography - A quantum signature of chaos
• Signatures of quantum chaos transition in short spin chains
• Quantum correlations as probes of chaos and ergodicity
• Optimal Pure-State Qubit Tomography via Sequential Weak Measurements
• Out-of-time-ordered correlators and the Loschmidt echo in the quantum kicked top: How low can we go?
• Quantum tomography with random diagonal unitary maps and statistical bounds on information generation using random matrix theory

Cited by in corpus (5)

• Witnessing quantum chaos using observational entropy
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• Loschmidt echo and scrambling of systematic errors in tomography -- a quantum signature of chaos
• Information acquisition, scrambling, and sensitivity to errors in quantum chaos