Conformal-field theory (CFT) code[1,2] 


Approximate code whose codewords lie in the low-energy subspace of a conformal field theory, e.g., the quantum Ising model at its critical point [1,2]. Its encoding is argued to perform source coding (i.e., compression) as well as channel coding (i.e., error correction) [1].


Code performance is quantified by a lower bound on the entanglement fidelity in terms of the conditional mutual information [1; Eq. (9)]; see also [3; Appx. A]. The coherent information of the combined noise and recover channel can also be perturbatively expanded [2].

Code Capacity Threshold

Threshold under dephasing depends on the structure of the conformal field theory, with the 1D critical Ising model admitting a finite threshold against certain dephasing noise [2].



F. Pastawski, J. Eisert, and H. Wilming, “Towards Holography via Quantum Source-Channel Codes”, Physical Review Letters 119, (2017) arXiv:1611.07528 DOI
S. Sang, T. H. Hsieh, and Y. Zou, “Approximate quantum error correcting codes from conformal field theory”, (2024) arXiv:2406.09555
K. Noh, V. V. Albert, and L. Jiang, “Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes”, IEEE Transactions on Information Theory 65, 2563 (2019) arXiv:1801.07271 DOI
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Zoo Code ID: cft

Cite as:
“Conformal-field theory (CFT) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.
@incollection{eczoo_cft, title={Conformal-field theory (CFT) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Conformal-field theory (CFT) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.