{"paper":{"title":"Fault-tolerant Coding for Quantum Communication","arxiv_id":"2009.07161","primary_cat":"quant-ph","submitted_at":"2020-09-15T15:10:50+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-1.13.0 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 v3","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.04,"main_claim_p":0.02,"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":1.0,"id":"s1","own":false,"role":"background","text":"When studying the optimal transmission rates achievable with asymptotically vanishing error it is usually assumed that these circuits can be implemented using noise-free gates.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.04,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.09,"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":0.89,"id":"s2","own":false,"role":"background","text":"While this assumption is satisfied for classical machines in many scenarios, it is not expected to be satisfied in the near term future for quantum machines where decoherence leads to faults in the quantum gates.","hedge":{"p":0.55,"label":"hedged_possibility"},"own_p":0.06,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.39,"role_probabilities":{"gap":0.11,"method":0.0,"result":0.0,"background":0.89,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.99,"id":"s3","own":false,"role":"gap","text":"As a result, fundamental questions regarding the practical relevance of quantum channel coding remain open.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.03,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.99,"method":0.0,"result":0.0,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":4,"p":0.97,"id":"s4","own":true,"role":"contribution","text":"By combining techniques from fault-tolerant quantum computation with techniques from quantum communication, we initiate the study of these questions.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.89,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.97,"interpretation":0.0}},{"i":5,"p":1.0,"id":"s5","own":true,"role":"contribution","text":"We introduce fault-tolerant versions of quantum capacities quantifying the optimal communication rates achievable with asymptotically vanishing total error when the encoding and decoding circuits are affected by gate errors with small probability.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.92,"main_claim_p":0.12,"quantitative":false,"quantitative_p":0.07,"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":6,"p":0.99,"id":"s6","own":true,"role":"result","text":"Our main results are threshold theorems for the classical and quantum capacity: For every quantum channel $T$ and every $\\epsilon>0$ there exists a threshold $p(\\epsilon,T)$ for the gate error probability below which rates larger than $C-\\epsilon$ are fault-tolerantly achievable with vanishing overall communication error, where $C$ denotes the usual 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