# Purity-testing stabilizer code[1]

## Description

A Galois-qudit stabilizer code that is constructed from a normal rational curve and that is relevant to testing the purity of an entangled Bell state stabilized by two parties [1].

## Parent

## Cousins

- Projective geometry code — Purity-testing stabilizer codes are constructed from normal rational curves.
- EA Galois-qudit stabilizer code — Purity-testing stabilizer codes are relevant to testing the purity of an entangled Bell state stabilized by two parties [1].
- Approximate secret-sharing code — The purity-testing protocol of Ref. [1] can be improved using approximate codes similar the approximate secret-sharing codes [2].

## References

- [1]
- H. Barnum et al., “Authentication of quantum messages”, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings. arXiv:quant-ph/0205128 DOI
- [2]
- M. Ben-Or et al., “Secure Multiparty Quantum Computation with (Only) a Strict Honest Majority”, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS’06) (2006) arXiv:0801.1544 DOI

## Page edit log

- Victor V. Albert (2024-07-27) — most recent

## Cite as:

“Purity-testing stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/purity_testing