Quantum Error-Correcting Codes Need Not Completely Reveal the Error Syndrome

John A. Smolin (UCLA); Peter W. Shor (AT&T Labs)

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Quantum Error-Correcting Codes Need Not Completely Reveal the Error Syndrome

Peter W. Shor (AT&T Labs), John A. Smolin (UCLA)

Quantum Physics · Submitted 8 Apr 1996

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

The authors' main claim We describe a code which does not find the complete error syndrome and can be used for reliable transmission of quantum information through channels which add more than one bit of entropy per transmitted bit.

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arXiv IDquant-ph/9604006 (version 2)

Pith IDVDY6ZUC7, Pith's permanent record of this paper and its review

CitationJohn A. Smolin (UCLA), Peter W. Shor (AT&T Labs). "Quantum Error-Correcting Codes Need Not Completely Reveal the Error Syndrome." arXiv:quant-ph/9604006 (1996). https://pith.science/paper/VDY6ZUC7

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What the abstract itself states, as probabilities: claims first 0.27 · states limitation 0.47 · human participants 0.01 · controlled comparison 0.49 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.98 · mentions code or data availability 0.03.

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

Quantum error-correcting codes so far proposed have not worked in the presence of noise which introduces more than one bit of entropy per qubit sent through a quantum channel, nor can any code which identifies the complete error syndrome. We describe a code which does not find the complete error syndrome and can be used for reliable transmission of quantum information through channels which add more than one bit of entropy per transmitted bit. In the case of the depolarizing channel our code can be used in a channel of fidelity .8096. The best existing code worked only down to .8107.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Quantum error-correcting codes so far proposed have not worked in the presence of noise which introduces more than one bit of entropy per qubit sent through a quantum channel, nor can any code which identifies the complete error syndrome.	background 0.65	0.08	0.14	asserted 1.00
s1	We describe a code which does not find the complete error syndrome and can be used for reliable transmission of quantum information through channels which add more than one bit of entropy per transmitted bit.	contribution 0.99	0.93	0.86	asserted 0.98
s2	In the case of the depolarizing channel our code can be used in a channel of fidelity .8096.	result 1.00	0.88	0.14	asserted 0.62
s3	The best existing code worked only down to .8107.	result 0.65	0.10	0.05	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.64 · evidence from proof or derivation 0.81.

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arXiv listing abstract v2

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T body sentences
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The paper

Original abstract

Quantum error-correcting codes so far proposed have not worked in the presence of noise which introduces more than one bit of entropy per qubit sent through a quantum channel, nor can any code which identifies the complete error syndrome. We describe a code which does not find the complete error syndrome and can be used for reliable transmission of quantum information through channels which add more than one bit of entropy per transmitted bit. In the case of the depolarizing channel our code can be used in a channel of fidelity .8096. The best existing code worked only down to .8107.

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References

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Distillation of secret key and entanglement from quantum states
quant-ph 2003-06 accept novelty 9.0 of 10

One-way public discussion achieves the wire-tapper secret-key rate for cqq states, and coherent key distillation achieves the coherent-information rate for one-way entanglement distillation.
Quantum incapacity from observable shadows
quant-ph 2026-07 accept novelty 8.0 of 10

A concrete qutrit channel has P=Q=0 at every blocklength while being neither PPT nor antidegradable, via a variance-dominating signed lift weaker than antidegradability.
A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
quant-ph 1996-04 accept novelty 8.0 of 10

An infinite family of quantum codes with n = 2^j physical qubits encoding n - j - 2 qubits against one error saturates the quantum Hamming bound exactly, constructed via a new stabilizer-group method.
A depolarizing choir sings in Gaussian harmony
quant-ph 2026-09 conditional novelty 7.0 of 10

The depolarizing channel acting on symmetric inputs converges to a Gaussian thermal attenuator, and optimized Gaussian codes yield the best-known depolarizing capacity threshold p≥0.2029161.
From Permutation Symmetry to Communication Bounds and Additivity
quant-ph 2026-10 conditional novelty 6.0 of 10

For permutation-invariant channel inputs, the optimized coherent information per use converges to the single-use maximum Q^(1)(N) at rate O(log n / sqrt n), giving a finite-block supremum and a strong converse for sym...

Show 1 more citing papers

On the iterative decoding of sparse quantum codes
quant-ph 2008-01 conditional novelty 6.0 of 10

Randomly breaking ties among degenerate errors lets belief propagation decode sparse quantum codes at depolarizing strengths roughly 40% higher than the unmodified algorithm.

How the literature uses it

19 arXiv papers cite this in 34 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 · 29 sentences without a confident label

Uses its method or tool 1 paper

The cat code used in [ref] is an $[[m,k=1]]_2$ CSS code with $k=k_1=1$ and $k_2=0$.

Randomized Dynamical Decoupling Strategies and Improved One-Way Key Rates for Quantum Cryptography · The Cat Code · 0.86

Uses its data or values 1 paper

Specifically, Shor and Smolin [ref] (concurrently with [ref] ) showed that by encoding with the $5$-qubit phase flip repetition code gives positive rate up to $p = 0.063452$.

Enhanced quantum capacity thresholds from symmetry · Previous Work · 0.85

Cites it as support 1 paper

Indeed, some numerical evidences clarified that the expressions in the capacity formulae are not additive [ref] , and the single letter characterization is not possible in general at least by using the same expressions.

Private and Quantum Capacities of More Capable and Less Noisy Quantum Channels · Introduction · 0.98

Cites it as background 1 paper

The phenomenon of degeneracy represents the most radical departure of quantum coding from classical coding [ref] .

Entanglement-assisted quantum turbo codes · EAQ Codes · 0.85

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