Upper Bounds on the Size of Entanglement-Assisted Codeword Stabilized Codes Using Semidefinite Programming

Ching Yi Lai, Pin Chieh Tseng, Wei Hsuan Yu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageEnglish
Title of host publication2024 IEEE International Symposium on Information Theory, ISIT 2024 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2269-2274
Number of pages6
ISBN (Electronic)9798350382846
DOIs
StatePublished - 2024
Event2024 IEEE International Symposium on Information Theory, ISIT 2024 - Athens, Greece
Duration: 7 Jul 202412 Jul 2024

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Conference

Conference2024 IEEE International Symposium on Information Theory, ISIT 2024
Country/TerritoryGreece
CityAthens
Period7/07/2412/07/24

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