TY - GEN
T1 - Upper Bounds on the Size of Entanglement-Assisted Codeword Stabilized Codes Using Semidefinite Programming
AU - Lai, Ching Yi
AU - Tseng, Pin Chieh
AU - Yu, Wei Hsuan
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024
Y1 - 2024
N2 - In this paper, we explore the application of semidef-inite programming to the realm of quantum codes, specifically focusing on codeword stabilized (CWS) codes with entanglement assistance. Notably, we utilize the isotropic subgroup of the CWS group and the set of word operators of a CWS-type quantum code to derive an upper bound on the minimum distance. Furthermore, this characterization can be incorporated into the associated distance enumerators, enabling us to construct semidefinite constraints that lead to SDP bounds on the minimum distance or size of CWS-type quantum codes. We illustrate several instances where SDP bounds outperform LP bounds.
AB - In this paper, we explore the application of semidef-inite programming to the realm of quantum codes, specifically focusing on codeword stabilized (CWS) codes with entanglement assistance. Notably, we utilize the isotropic subgroup of the CWS group and the set of word operators of a CWS-type quantum code to derive an upper bound on the minimum distance. Furthermore, this characterization can be incorporated into the associated distance enumerators, enabling us to construct semidefinite constraints that lead to SDP bounds on the minimum distance or size of CWS-type quantum codes. We illustrate several instances where SDP bounds outperform LP bounds.
UR - http://www.scopus.com/inward/record.url?scp=85202834165&partnerID=8YFLogxK
U2 - 10.1109/ISIT57864.2024.10619303
DO - 10.1109/ISIT57864.2024.10619303
M3 - Conference contribution
AN - SCOPUS:85202834165
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2269
EP - 2274
BT - 2024 IEEE International Symposium on Information Theory, ISIT 2024 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2024 IEEE International Symposium on Information Theory, ISIT 2024
Y2 - 7 July 2024 through 12 July 2024
ER -