\([[5,1,3]]_{\mathbb{R}}\) Braunstein five-mode code[1] 

Description

An analog stabilizer version of the five-qubit perfect code, encoding one mode into five and correcting arbitrary errors on any one mode.

Decoding

Error correction can be done using linear-optical elements and feedback [2].

Parents

Cousin

References

[1]
S. L. Braunstein, “Error Correction for Continuous Quantum Variables”, Physical Review Letters 80, 4084 (1998) arXiv:quant-ph/9711049 DOI
[2]
S. L. Braunstein, “Quantum error correction for communication with linear optics”, Nature 394, 47 (1998) DOI
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Zoo Code ID: braunstein

Cite as:
“\([[5,1,3]]_{\mathbb{R}}\) Braunstein five-mode code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/braunstein
BibTeX:
@incollection{eczoo_braunstein, title={\([[5,1,3]]_{\mathbb{R}}\) Braunstein five-mode code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/braunstein} }
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Cite as:

“\([[5,1,3]]_{\mathbb{R}}\) Braunstein five-mode code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/braunstein

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/stabilizer/hyperplane/braunstein.yml.