Quantum Reed-Muller Codes

[ChrisPattison]

The page on Quantum Reed-Muller codes codes/quantum/qubits/rm/quantum_reed_muller.yml claims that

Additionally, CSS codes formed from binary Reed-Muller codes achieve channel capacity on erasure channels [2].

This cites a result about classical Reed-Muller codes on classical erasure channels. I'm not sure how this could follow in a straightforward way from this paper. It's worth noting that the capacity of the quantum erasure channel isn't even positive for erasure fraction greater than 1/3

[valbert4]

Thanks for pointing this out. I meant this ref: 10.1109/ISIT.2016.7541599 <https://doi.org/10.1109/ISIT.2016.7541599> Best, Victor

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On Fri, Nov 10, 2023 at 5:53 AM Chris Pattison ***@***.***> wrote: The page on Quantum Reed-Muller codes codes/quantum/qubits/rm/quantum_reed_muller.yml claims that Additionally, CSS codes formed from binary Reed-Muller codes achieve channel capacity on erasure channels [2] <https://errorcorrectionzoo.org/c/quantum_reed_muller#citation-2>. This cites a result about classical Reed-Muller codes on classical erasure channels <https://arxiv.org/abs/1601.04689>. I'm not sure how this could follow in a straightforward way from this paper. It's worth noting that the capacity of the quantum erasure channel isn't even positive for erasure fraction greater than 1/3 <https://arxiv.org/abs/quant-ph/9701015> — Reply to this email directly, view it on GitHub <#336>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACCCKUR3IMFPM7M624V4YI3YDYBRJAVCNFSM6AAAAAA7F7SZO2VHI2DSMVQWIX3LMV43ASLTON2WKOZRHE4DOMZYHE3DSNI> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>