{"paper":{"title":"An Instability of the Quantum Markov Length","arxiv_id":"2610.12929","primary_cat":"quant-ph","submitted_at":"2026-10-09T03:19:23+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"The Markov length, the length scale governing the exponential decay of conditional mutual information (CMI) in a quantum many-body state, has proven useful for characterizing mixed-state phases of matter.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.06,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.92,"id":"s1","own":true,"role":"result","text":"Nevertheless, we show that a state's Markov length is not generally stable under weak local channels.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.87,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.01,"method":0.0,"result":0.92,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.07,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"result","text":"The failure of stability occurs already at a pure product state.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.79,"main_claim_p":0.27,"quantitative":false,"quantitative_p":0.13,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.79,"id":"s3","own":true,"role":"result","text":"We demonstrate this explicitly in a one-dimensional fermionic chain, where a fine-tuned depth-two circuit of nearest-neighbor Gaussian channels maps the vacuum to a state whose CMI decays \\emph{algebraically} and whose Markov length is therefore infinite, even when the channels are taken arbitrarily close to the identity.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.2,"quantitative":true,"quantitative_p":0.82,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.79,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.18,"interpretation":0.0}},{"i":4,"p":0.9,"id":"s4","own":true,"role":"interpretation","text":"The algebraic decay is rooted in the nonanalyticity of the von Neumann entropy at rank-deficient density operators.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.8,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.1,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.9}},{"i":5,"p":0.84,"id":"s5","own":true,"role":"result","text":"We exhibit an analogous instability on an ordinary qubit chain.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.84,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.16,"interpretation":0.0}},{"i":6,"p":0.97,"id":"s6","own":true,"role":"result","text":"More generally, we show that the Markov length is unstable in any translation-invariant state with even a single rank-deficient reduced density operator.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.41,"quantitative":false,"quantitative_p":0.29,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.97,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.0}},{"i":7,"p":1.0,"id":"s7","own":false,"role":"interpretation","text":"These results pose a challenge to recent definitions of mixed-state phase equivalence based on the Markov 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