- Open Access
Quantum observables over time for information recovery
Phys. Rev. Research 8, 033208 – Published 19 August, 2026
DOI: https://doi.org/10.1103/schg-nl3m
Abstract
We introduce the concept of quantum observables over time (QOOT), an operator that jointly describes two observables at two distinct time points, as a dual of the quantum state over time formalism. We provide a full characterization of the conditions under which a QOOT can be properly defined, via a no-go theorem. We use QOOTs to establish a notion of time reversal for generic quantum channels with respect to a reference observable, enabling the systematic construction of recovery maps that preserve the latter. These recovery maps, although generally nonphysical, can be decomposed into realizable channels, enabling their application in noiseless expectation value estimation tasks. We provide explicit examples and compare our protocol with other error mitigation methods. We show that our protocol retrieves the noiseless expectation value of the reference observable and can achieve optimal sampling overhead, outperforming probabilistic error cancellation.
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