Asymptotic Replacement for Quantum Channel Products with Applications to Inhomogeneous Matrix Product States
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Quantum Physics arXiv:2605.00157 (quant-ph) [Submitted on 30 Apr 2026] Title:Asymptotic Replacement for Quantum Channel Products with Applications to Inhomogeneous Matrix Product States Authors:Lubashan Pathirana View a PDF of the paper titled Asymptotic Replacement for Quantum Channel Products with Applications to Inhomogeneous Matrix Product States, by Lubashan Pathirana View PDF HTML (experimental) Abstract:We develop a product-level trace-Dobrushin theory for finite-dimensional quantum channel products and apply it to deterministic and stationary random inhomogeneous matrix product states in left-canonical CPTP gauge. For a product of channels, the centered trace-Dobrushin coefficient quantifies the residual dependence on the input state, and its decay is the criterion for trace-norm forgetting. In the deterministic setting, this decay is equivalent to asymptotic replacement by a moving replacement channel. For two-sided products, pullback forgetting produces a unique boundary state, which determines the canonical replacement family. For stationary random CPTP cocycles, submultiplicativity of the product coefficient yields a trace-Dobrushin Lyapunov exponent. We prove that the almost sure negativity of this exponent is equivalent to quenched trace-norm memory loss and gives exponential forward and pullback convergence to a unique dynamically stationary random replacement channel. When the \(\varrho\)-mixing profile of the channel environment tends to zero, we obtain annealed super-polynomial estimates, while independence gives annealed exponential estimates. Finally, we transfer these estimates to inhomogeneous matrix product states whose auxiliary transfer maps are CPTP. These channel estimates transfer to deterministic and stationary random inhomogeneous MPS, giving infinite-volume limits of trace-closed finite-volume states, quantitative boundary stability, and correlation bounds governed by the same auxiliary product coefficients. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Probability (math.PR) Cite as: arXiv:2605.00157 [quant-ph] (or arXiv:2605.00157v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.00157 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Lubashan Pathirana [view email] [v1] Thu, 30 Apr 2026 19:26:11 UTC (75 KB) Full-text links: Access Paper: View a PDF of the paper titled Asymptotic Replacement for Quantum Channel Products with Applications to Inhomogeneous Matrix Product States, by Lubashan PathiranaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math-ph math.MP math.PR References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)