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arXiv:1808.04375 · Physical Review Research

Sensitivity of quantum information to environment perturbations measured with a nonlocal out-of-time-order correlation function

Mohamad Niknam, Léa Ferreira dos Santos, David G. Cory

Published Feb 24, 2020• 68 citations
arXivHTMLPDF

Abstract

This work shows that by exploring the collective response of a many-body nuclear-spin system, the correlation between various parts of it can be studied. The appearance of the higher correlation orders, as a qubit shares its quantum information with the surrounding qubits, is used to measure quantum information flow.
DOI
10.1103/physrevresearch.2.013200

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Understanding the flow, loss, and recovery of the information between a system and its environment is essential for advancing quantum technologies. The central spin system serves as a useful model for a single qubit, offering valuable insights into how quantum systems can be manipulated and protected from decoherence. This work uses the stimulated echo experiment to track the information flow between the central spin and its environment, providing a direct measure of the sensitivity of system/environment correlations to environmental dynamics. The extent of mixing and the growth of correlations are quantified through autocorrelation functions of the noise and environmental dynamics, which also enable the estimation of nested commutators between the system/environment and environmental Hamiltonians. Complementary decoupling experiments offer a straightforward measure of the strength of the system Hamiltonians. The approach is experimentally demonstrated on a spin system.
We provide a general protocol to measure out-of-time-order correlation functions. These correlation functions are of broad theoretical interest for diagnosing the scrambling of quantum information in interacting quantum systems and have recently received particular attention in the study of chaos and black holes within holographic duality. Measuring them requires an echo-type sequence in which the sign of a many-body Hamiltonian is reversed. We illustrate our protocol by detailing an implementation employing cold atoms and cavity quantum electrodynamics to probe spin models with nonlocal interactions. To verify the feasibility of the scheme with current technology, we analyze the effects of dissipation in a chaotic kicked-top model. Finally, we propose a number of other experimental platforms where similar out-of-time-order correlation functions can be measured.
Abstract Advances in quantum information processing can open a way for numerous applications of the processing in various fields of science and technology: communication, precision measurement, computing, nano-scale detectors, and sensors. Classical and various quantum correlations have been studied in real spin 1/2 systems. The nonlocality measures provide a novel classification scheme for bipartite states, highlighting that nonlocality is a quantum resource distinct from other types of quantum correlations. We first studied the temperature and field dependencies of nonlocality measure in the three fictitious spin 1/2 system, which represents a nuclear spin-7/2 placed in magnetic and inhomogeneous electric fields. The relationship between nonlocality and other quantum correlations (entanglement and geometric discord) was studied. The Hamiltonian and spin operators for a spin 7/2 are represented in the basis formed by the Kronecker products of the Pauli matrices. This transformation allows us to represent a spin 7/2 as a system of three coupled fictitious spins 1/2 and, from the quantum information point of view, as an equivalent system of three coupling qubits. Well-developed methods were used to calculate measures of quantum correlations. For example, we consider 59Co (spin 7/2) in the compounds [Co(NH3)5Cl]Cl2 and Ca3Co2O6. The interaction between the fictitious spins of 59Co nuclei depends on the magnitude and direction of the external magnetic field. Other potential cases of quantum correlations can be realized based on nuclear spins 7/2 in solid-state systems, for instance, such as 51V, 165Ho, or 123Sb.
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Correlations of fluctuations are the driving forces behind the dynamics and thermodynamics in quantum many-body systems. For qubits embedded in a quantum bath, the correlations in the bath are key to understanding and combating decoherence-a critical issue in quantum information technology. However, there is no systematic method for characterizing the many-body correlations in quantum baths beyond the second order or the Gaussian approximation. Here we present a scheme to characterize the correlations in a quantum bath to arbitrary order. The scheme employs a weak measurement of the bath via the projective measurement of a central system. The bath correlations, including both the "classical" and the "quantum" parts, can be reconstructed from the correlations of the measurement outputs. The possibility of full characterization of many-body correlations in a quantum bath forms the basis for optimizing quantum control against decoherence in realistic environments, for studying the quantum characteristics of baths, and for the quantum sensing of correlated clusters in quantum baths.