\(((n,2,2))\) Bravyi-Lee-Li-Yoshida PI code[1]
Description
PI distance-two code on \(n\geq4\) qubits whose degree of entanglement vanishes asymptotically with \(n\) [1; Appx. D] (cf. [2]).
In terms of Dicke states, the codewords are \begin{align} \begin{split} |0_{L}\rangle&=\sqrt{1-\frac{2}{n}}|D_{0}^{n}\rangle+\sqrt{\frac{2}{n}}|D_{n}^{n}\rangle\\ |1_{L}\rangle&=|D_{2}^{n}\rangle~. \end{split} \tag*{(1)}\end{align}
Cousin
- Concatenated qubit code— The Bravyi-Lee-Li-Yoshida PI code can be concatenated to yield codes that have higher distance and that admit codewords with vanishing entanglement [1; Appx. D] (cf. [2]).
Primary Hierarchy
Parents
The \(((n,2,2))\) PI code is a Movassagh-Ouyang Hamiltonian code constructed from a binary code consisting of all codewords of weight 0, 2, or \(n\) [1; Appx. D].
\(((n,2,2))\) Bravyi-Lee-Li-Yoshida PI code
Children
The Bravyi-Lee-Li-Yoshida code reduces to the four-qubit single-deletion code for \(n=4\).
References
- [1]
- S. Bravyi, D. Lee, Z. Li, and B. Yoshida, “How Much Entanglement Is Needed for Quantum Error Correction?”, Physical Review Letters 134, (2025) arXiv:2405.01332 DOI
- [2]
- G. Gour and N. R. Wallach, “Entanglement of subspaces and error-correcting codes”, Physical Review A 76, (2007) arXiv:0704.0251 DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2024-02-07)
Cite as:
“\(((n,2,2))\) Bravyi-Lee-Li-Yoshida PI code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/unentangled_permutation_invariant, arXiv:2606.11484