{"paper":{"title":"Non-equilibrium equalities with unital quantum channels","arxiv_id":"1301.0855","primary_cat":"quant-ph","submitted_at":"2013-01-05T02:04:31+00:00","version_compiled":"v3"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13-20260917 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 v3","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"A general tool for description of open quantum systems is given by the formalism of quantum operations.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.12,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.03,"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":1.0,"id":"s1","own":false,"role":"background","text":"Most important of them are trace-preserving maps also known as quantum channels.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.2,"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":2,"p":0.97,"id":"s2","own":true,"role":"contribution","text":"We discuss those conditions on quantum channels under which the Jarzynski equality and related fluctuation theorems hold.","hedge":{"p":0.65,"label":"asserted"},"own_p":0.67,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.03,"limitation":0.0,"future_work":0.0,"contribution":0.97,"interpretation":0.0}},{"i":3,"p":0.79,"id":"s3","own":true,"role":"result","text":"It is essential that the representing quantum channel be unital.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.58,"main_claim_p":0.45,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.79,"background":0.03,"limitation":0.04,"future_work":0.0,"contribution":0.1,"interpretation":0.03}},{"i":4,"p":0.52,"id":"s4","own":true,"role":"result","text":"Under the mentioned condition, we first derive the corresponding Jarzynski equality.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.19,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.52,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.45,"interpretation":0.0}},{"i":5,"p":0.67,"id":"s5","own":true,"role":"result","text":"For bistochastic map and its adjoint, we further formulate a theorem of Tasaki-Crooks type.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.67,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.33,"interpretation":0.0}},{"i":6,"p":0.92,"id":"s6","own":true,"role":"contribution","text":"In the context of unital channels, some notes on heat transfer between two quantum systems are given.","hedge":{"p":0.72,"label":"asserted"},"own_p":0.73,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.06,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.92,"interpretation":0.02}},{"i":7,"p":1.0,"id":"s7","own":true,"role":"contribution","text":"We also consider the case of a finite system operated by an external agent with a feedback control.","hedge":{"p":0.86,"label":"asserted"},"own_p":0.75,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":8,"p":0.86,"id":"s8","own":true,"role":"result","text":"When unital channels are applied at the first stage and, for a mutual-information form, at the further ones, we obtain quantum Jarzynski-Sagawa-Ueda relations.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.26,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.86,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.14,"interpretation":0.0}},{"i":9,"p":0.74,"id":"s9","own":true,"role":"interpretation","text":"These are extension of the previously given results to unital quantum 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