Time‐Symmetric Correlations for Open Quantum Systems

The statistics of sequential measurements of two non‐commuting observables typically depends on the order in which they are measured. However, if a system evolves unitarily between sequential measurements of dichotomic observables (i.e., observables whose measurement outcomes are labeled by ), then the expectation value of the product of the sequential measurements is in fact independent of the order of the measurements, provided that one uses the inverse unitary for the opposite order. In this work, a quantum Bayes' rule is used to show that the aforementioned time symmetry for sequential measurements of dichotomic observables extends to open quantum systems that evolve according to a general quantum channel between measurements. Such results are quite striking in light of the standard view that open quantum systems—which may lose information to their environment—are not reversible in any operational sense. An example of such time‐symmetric correlations is given for the amplitude‐damping channel, where it is observed that the symmetry is realized by a reverse channel that is a combination of the Petz recovery map together with a dephasing channel.