  Quantum many-body systems are characterized by their correlations. While
equal-time correlators and unequal-time commutators between operators are
standard observables, the direct access to unequal-time anti-commutators poses
a formidable experimental challenge. Here, we propose a general technique for
measuring unequal-time anti-commutators using the linear response of a system
to a non-Hermitian perturbation. We illustrate the protocol at the example of a
Bose-Hubbard model, where the approach to thermal equilibrium in a closed
quantum system can be tracked by measuring both sides of the
fluctuation-dissipation relation. We relate the scheme to the quantum Zeno
effect and weak measurements, and illustrate possible implementations at the
example of a cold-atom system. Our proposal provides a way of characterizing
dynamical correlations in quantum many-body systems with potential applications
in understanding strongly correlated matter as well as for novel quantum
technologies.
