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The capacity of the noisy quantum channel

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Seth Lloyd (MIT Mechanical Engineering)

Quantum Physics · Submitted 19 Apr 1996

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel.

how it is stated · asserted 1.00 read the record →

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arXiv IDquant-ph/9604015 (version 2)
Pith IDKSXRQ3HC, Pith's permanent record of this paper and its review
CitationSeth Lloyd (MIT Mechanical Engineering). "The capacity of the noisy quantum channel." arXiv:quant-ph/9604015 (1996). https://pith.science/paper/KSXRQ3HC
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,845 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.57 · compares with prior results 0.85 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel. A class of quantum error-correcting codes is presented that allow the information transmitted to attain this limit. The result is the quantum analog of Shannon's bound and code for the noisy classical channel.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel. result 0.86 0.86 0.59 asserted 1.00
s1 A class of quantum error-correcting codes is presented that allow the information transmitted to attain this limit. contribution 0.86 0.91 0.31 asserted 1.00
s2 The result is the quantum analog of Shannon's bound and code for the noisy classical channel. interpretation 0.98 0.50 0.21 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel. A class of quantum error-correcting codes is presented that allow the information transmitted to attain this limit. The result is the quantum analog of Shannon's bound and code for the noisy classical channel.

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References
How later papers used it

125 later papers cite it

Evidence: some. 124 of the citing papers share no author with it, and 6 of those carry a confident label from Pith's citation classifier.

Pith read 4 of the 170 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 1 of 3 papers with this label
How the literature uses it

26 arXiv papers cite this in 33 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 14 sentences without a confident label

Builds on it 1 paper
  • 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] .

    Extendibility limits the performance of quantum processors · Introduction · 0.85

Cites it as background 17 papers
  • 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.

    Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel · Communication tasks · 0.88

  • 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.

    Unbounded number of channel uses are required to see quantum capacity · Introduction · 0.98

  • 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: $N(ρ) = tr_E(U ρU^y)$.

    When does noise increase the quantum capacity? · Introduction · 0.92

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