{"arxiv_id":"quant-ph/9604015","incoming":{"papers":26,"sentences":33,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2108.03137","title":"Extendibility limits the performance of quantum processors","url":"/paper/2108.03137","section":"Introduction","sentence":"This kind of task was defined and developed in [ref] , albeit with the assistance of a particular kind of $k$-extendible channel and only the case $k=2$ was considered there, generalizing the usual notion of entanglement distillation and quantum communication protocols from [ref] .","intent_p":0.85,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":17,"sentences":18,"quotes":[{"arxiv_id":"1604.07974","title":"Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel","url":"/paper/1604.07974","section":"Communication tasks","sentence":"The quantum capacity characterizes the ability of a quantum channel for this task in the absence of additional resources [ref] [equation] where $^(1)() = max_ϕ^AA'^(1)(,ϕ^AA')$ is the coherent information of a quantum channel.","intent_p":0.88,"contests_p":null},{"arxiv_id":"1408.5115","title":"Unbounded number of channel uses are required to see quantum capacity","url":"/paper/1408.5115","section":"Introduction","sentence":"It has been known for some time [ref] that the quantum capacity is given by a regularised expression—the optimisation of an entropic quantity (the coherent information) in the limit of arbitrarily many uses of the channel: [equation] (Here, $Q^(n)()$ is the coherent information $$ maximised over a joint input $ρ^(n)$ for $n$ uses of the channel $$.) However, the regularisation renders computing the quantum capacity infeasible; it involves an optimisation over an infinite parameter space.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1107.4385","title":"When does noise increase the quantum capacity?","url":"/paper/1107.4385","section":"Introduction","sentence":"The quantum capacity is known to be lower bounded by the coherent information [ref] : Q(N)≥I_c(A⟩B) :=max_ρ(S(B)_σ-S(E)_σ), where the von Neumann entropies are evaluated on $σ_BE = U ρU^†$, with $U : A ↦BE$ the isometry associated to the channel $N$ as follows: $N(ρ) = tr_E(U ρU^y)$.","intent_p":0.92,"contests_p":null},{"arxiv_id":"2205.05736","title":"Exact solution for the quantum and private capacities of bosonic dephasing channels","url":"/paper/2205.05736","section":"Introduction","sentence":"Here, a key quantity of interest is the quantum capacity $Q(_p)$ of the bosonic dephasing channel $_p$, which is equal to the largest rate at which quantum information can be faithfully sustained in the presence of dephasing, such that the error probability of decoding correctly decreases to zero as the number of channel uses becomes large [ref] .","intent_p":0.9,"contests_p":null},{"arxiv_id":"1705.08878","title":"Quantum Channel Capacities Per Unit Cost","url":"/paper/1705.08878","section":"Quantum Communication","sentence":"Quantum capacity was first studied in [ref] when there is no cost constraint and recently in [ref] when there is a cost constraint.","intent_p":0.97,"contests_p":null}]}],"unlabelled_sentences":14},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":{"arxiv_id":"quant-ph/9604015","kind":"model","paper_version":2,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T16:00:38+00:00","loaded_at":"2026-10-28T01:02:34.241980+00:00","evidence":"some","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":1,"entries":[{"p":0.94,"quote":{"text":"We quantify this information using the coherent information [ref] .","citing":"2401.17066","section":"Echo protocol"},"citing":[{"self":false,"year":2024,"title":"Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity","arxiv_id":"2401.17066"}],"verified":true,"paraphrase":"Used the coherent information from this paper to quantify the information Bob has about the state Alice prepared."}],"papers_all":3,"self_papers":0,"self_entries":[]}],"counts":{"by_kind":{"extends":2,"method_or_tool":3,"supports_this_paper":1},"dropped":{"relied_on":0,"unknown_ids":0,"account_lines":0,"contest_vetoed":0,"below_threshold":0,"contest_drawback":0,"contest_without_basis":0,"contest_not_one_sentence":0,"contest_on_group_citation":0},"papers_read":3,"self_papers":1,"citing_papers":125,"sentences_read":4,"citing_sentences":170,"unambiguous_read":4,"typed_independent":6,"independent_papers":124,"by_kind_independent":{"extends":2,"method_or_tool":3,"supports_this_paper":1}},"input_sha256":"ebbd1de31cfe3d5a2fced6eeff444f7223fe4d4b26d127a4da67efd0689648cf","method":"For a paper with five or more citing arXiv papers, Pith selected up to 40 citing sentences its citation classifier typed, read those whose citation markers point at this paper alone, and wrote one paraphrase for each later paper in each group, each resting on one sentence. A later paper is listed under a label only when the classifier gives one of its sentences that label at intent probability 0.8 or more (0.95 for support), Pith's reading of the sentence finds that the citing paper itself did it, and a second check of the paraphrase against the sentence passes. The section lists uses only: building on the paper, using its method, tool, data or values, comparing with it and citing it as support. It does not list criticism or disagreement, so their absence says nothing about how the paper has been received. Code counted the papers, wrote the summary from the listed entries, set the evidence level and linked each entry to its citing paper. Quotes are copied from the citing sentence and shown only when the citing paper's licence is CC BY, CC BY-SA or CC0; otherwise the paraphrase is shown. Papers that share an author with this one are listed apart. A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"1 later paper by other authors is listed below: 1 used its method or tool."},"_links":{"html":"https://pith.science/paper/quant-ph/9604015"}}