Characterization of Arbitrary-Order Correlations in Quantum Baths by Weak Measurement

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.

Figure 1

Weak measurement for reconstruction of bath correlations. (a) A unit sequence (to be repeated many times) of $N$ weak measurements at different times for reconstructing the bath correlations at the $N$th order. (b) Realization of a weak measurement on the bath via the projective measurement of the central system. (c) Reconstruction of the bath correlations by selecting a subset of outputs from a long measurement sequence, with the unused outputs in between taken as “idle” (I).