Does the Physical Bridge between operator autocorrelation and measurement statistics survive non-Markovian noise?

Does the Physical Bridge between operator autocorrelation and measurement statistics survive non-Markovian noise? Ask Question Asked 2 days ago Modified yesterday Viewed 29 times 2 In a recent paper on Krylov-based error diagnostics for open quantum systems, I proved that the Physical Bridge C_meas(τ) ∝ C_op(τ) holds under arbitrary Markovian (Lindblad) dissipation, verified numerically with Pearson r > 0.99 across dephasing, amplitude damping, and depolarizing channels. The derivation relies on the Haar-average identity and trace-preservation of the Lindblad map. For non-Markovian noise, where the environment has memory and the evolution cannot be written as a one-parameter semigroup, these properties no longer hold in general. My question: Is there a known result (or counterexample) for whether the proportionality C_meas ∝ C_op survives under non-Markovian dynamics, e.g. described by a time-convolutionless master equation or a Nakajima-Zwanzig kernel? Relevant paper and code: https://zenodo.org/records/18959827 https://github.com/quantumspiritresearch-crypto/qkd-krylov-detector error-correctionopen-quantum-systems Share Improve this question Follow asked 2 days ago Daniel Süß 212 2 bronze badges New contributor Add a comment 1 Answer Sorted by: Highest score (default) Date modified (newest first) Date created (oldest first) 0 The proportionality between measured correlations and operator autocorrelations is usually justified by the quantum regression theorem (QRT). When the system dynamics is Markovian and described by a Lindblad-type master equation, the theorem implies that multi-time correlations evolve with the same dynamical generator as single-time expectation values. Under these conditions the measured correlation function can be proportional to the corresponding operator correlation. For genuinely non-Markovian dynamics this relation does not generally hold. Multi-time correlations then depend on environmental memory and on system–environment correlations that are not captured by the reduced master equation, so the quantum regression theorem can fail. However, the proportionality between measurement correlations and operator correlations is not restricted strictly to Markovian systems. It can still arise in several situations where the measurement effectively probes a dynamically closed or effectively Markovian sector of the dynamics. Examples include: Pure dephasing models: the environment causes only phase noise without mixing the measured observable with other operators, so the observable sector remains closed even if the bath has memory. Reaction coordinate descriptions: part of the environment can be incorporated into an enlarged system whose dynamics is approximately Markovian, even though the reduced dynamics of the original system appears non-Markovian. Effective Markovian embeddings: some non-Markovian evolutions can be represented as Markovian dynamics in a larger Hilbert space, and if the measurement probes only a restricted observable subspace the resulting correlations can still follow the operator autocorrelations. So the relation between measured correlations and operator autocorrelations is guaranteed in Markovian dynamics but may also appear in certain structured non-Markovian models when the measurement effectively sees a closed or effectively Markovian part of the dynamics. Share Improve this answer Follow edited yesterday answered yesterday Matti Sarjala 3362 2 silver badges 9 9 bronze badges Thank you, the QRT connection is exactly what I was looking for. My derivation in the related paper uses Haar-averaging and trace-preservation, which is consistent with the QRT but from a different angle. The non-Markovian exceptions you mention are useful directions for the open question. –  Daniel Süß Commented yesterday Add a comment Your Answer Sign up or log in Sign up using Google Sign up using Email and Password Post as a guest Name Email Required, but never shown Post Your Answer By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions error-correctionopen-quantum-systems See similar questions with these tags. The Overflow Blog Open source for awkward robots Domain expertise still wanted: the latest trends in AI-assisted knowledge for... 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