bibkey: lonigrochruscinski2022dephasing
authors: Davide Lonigro; Dariusz Chruściński
year: 2022
title: "On the classicality of quantum dephasing processes"
doi: 10.3389/frqst.2022.1090022
url: https://arxiv.org/abs/2211.02014v2
claim: "The paper studies the multitime statistics of pure dephasing systems probed by repeated sharp measurements, proves that a diagonal initial state measured in a phase-modified Fourier basis of Eq. eq:mubs, which is unbiased with respect to the dephasing basis, gives a 2-classical process for every environment, and conjectures that, apart from a maximally mixed initial state, this is the only measurement choice yielding a genuinely time-dependent 2-classical process."
strata_touched:
  - D5/S3/Quantum/Decoherence/DephasingTwoClassicalityBlockRefutation
license: citation-only
triage: anchor

On the classicality of quantum dephasing processes

D. Lonigro and D. Chruściński, arXiv:2211.02014v2 [quant-ph, math-ph]; Frontiers in Quantum Science and Technology 1, 1090022 (2022). Quotations are from the v2 TeX source.

The classicality notion:

$N$-\textit{classical}, if Eq.~\eqref{eq:consistency} is satisfied for all $n=1,\dots ,N$.

The conjecture, after Proposition prop:2classicality_mubs:

It may be conjectured that this is the only measurement choice yielding a genuinely time-dependent $2$-classical process—excepting the particular case in which ${\rho }_{t_0}$ is maximally mixed, cf.~the discussion in the next subsection.

Verified locator

Source: https://arxiv.org/abs/2211.02014v2

• URL: https://arxiv.org/abs/2211.02014v2 (source dephasing-v2.tex, md5 e2904085775dc9d0af3b2dba4d50c065):
  • the multitime statistics and the consistency condition, l. 72–84;
  • $N$-classicality, l. 88–90;
  • dephasing Hamiltonians and their multitime statistics, l. 128–146;
  • fully compatible measurements and genuine time dependence, l. 201;
  • the qubit results and their extra hypotheses, l. 244–273;
  • the unbiased bases and Proposition prop:2classicality_mubs, l. 277–346;
  • the conjecture, l. 347.
• DOI: 10.3389/frqst.2022.1090022 (https://doi.org/10.3389/frqst.2022.1090022; Crossref lists Frontiers in Quantum Science and Technology, volume 1, article 1090022, published 19 December 2022).