\([[5,1,3]]_{\mathbb{R}}\) Braunstein five-mode code[1]
Alternative names: Five-wavepacket code.
Description
An analog stabilizer version of the five-qubit perfect code, encoding one mode into five and correcting arbitrary errors on any one mode.Encoding
Seven beam splitters [2].Decoding
Error correction can be done using linear-optical elements and feedback [3].Cousin
- \([[5,1,3]]_{\mathbb{Z}_q}\) modular-qudit code— The Braunstein five-mode code is a bosonic analogue of the five-qudit code.
Primary Hierarchy
Parents
Braunstein five-mode codewords are CV AME [4].
\([[5,1,3]]_{\mathbb{R}}\) Braunstein five-mode code
References
- [1]
- S. L. Braunstein, “Error Correction for Continuous Quantum Variables”, Physical Review Letters 80, 4084 (1998) arXiv:quant-ph/9711049 DOI
- [2]
- T. A. Walker and S. L. Braunstein, “Five-wave-packet linear optics quantum-error-correcting code”, Physical Review A 81, (2010) DOI
- [3]
- S. L. Braunstein, “Quantum error correction for communication with linear optics”, Nature 394, 47 (1998) DOI
- [4]
- J. I. Kwon, A. J. Brady, and V. V. Albert, “Most continuous-variable cluster states are too entangled to be useless”, (2025) arXiv:2503.15698
Page edit log
- Victor V. Albert (2022-06-22) — most recent
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