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

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arxiv quant-ph/9604006 v2 pith:VDY6ZUC7 submitted 1996-04-08 quant-ph

Peter W. Shor (AT&T Labs) , John A. Smolin (UCLA) This is my paper · ORCID
classification quant-ph
keywords codequantumchannelerrorsyndromecodescompleteentropy
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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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Cited by 1 Pith paper

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  1. Quantum Incapacity beyond No-Cloning and PPT Mechanisms

    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.

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