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Quantum many-body systems are characterized by their correlations. Whileequal-time correlators and unequal-time commutators between operators arestandard observables, the direct access to unequal-time anti-commutators posesa formidable experimental challenge. Here, we propose a general technique formeasuring unequal-time anti-commutators using the linear response of a systemto a non-Hermitian perturbation. We illustrate the protocol at the example of aBose-Hubbard model, where the approach to thermal equilibrium in a closedquantum system can be tracked by measuring both sides of thefluctuation-dissipation relation. We relate the scheme to the quantum Zenoeffect and weak measurements, and illustrate possible implementations at theexample of a cold-atom system. Our proposal provides a way of characterizingdynamical correlations in quantum many-body systems with potential applicationsin understanding strongly correlated matter as well as for novel quantumtechnologies.

From Non-Hermitian Linear Response to Dynamical Correlations and Fluctuation-Dissipation Relations in Quantum Many-Body Systems