Semidefinite programming bounds on the size of entanglement-assisted
codeword stabilized quantum codes
- URL: http://arxiv.org/abs/2311.07111v1
- Date: Mon, 13 Nov 2023 07:01:58 GMT
- Title: Semidefinite programming bounds on the size of entanglement-assisted
codeword stabilized quantum codes
- Authors: Ching-Yi Lai and Pin-Chieh Tseng and Wei-Hsuan Yu
- Abstract summary: We use 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.
This characterization can be incorporated into the associated distance enumerators, enabling us to construct semidefinite constraints.
We illustrate several instances where SDP bounds outperform LP bounds, and there are even cases where LP fails to yield meaningful results.
- Score: 5.770351255180495
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper, we explore the application of semidefinite 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, and there are even cases where
LP fails to yield meaningful results, while SDP consistently provides tight and
relevant bounds. Finally, we also provide interpretations of the Shor-Laflamme
weight enumerators and shadow enumerators for codeword stabilized codes,
enhancing our understanding of quantum codes.
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