Linear programming bounds for entanglement-assisted quantum codes

Ching-Yi Lai, Alexei Ashikhmin

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

Abstract

In this paper, we define two split weight enumerators for general quantum codes with entanglement assistance, including nonadditive codes. We show that they obey a MacWilliams identity, which allows us to prove algebraic linear programming bounds, such as the Singleton bound, the Hamming bound, and the first linear programming bound. On the other hand, we derive additional constraints on the size of Pauli subgroups for quantum codes, which helps to improve the linear programming bounds on the minimum distance of quantum codes of small length.

Original languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3200-3204
Number of pages5
ISBN (Electronic)9781509040964
DOIs
StatePublished - 9 Aug 2017
Event2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany
Duration: 25 Jun 201730 Jun 2017

Publication series

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

Conference

Conference2017 IEEE International Symposium on Information Theory, ISIT 2017
CountryGermany
CityAachen
Period25/06/1730/06/17

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