Single Error Correcting Quantum Codes for the Amplitude Damping Channel Based on Classical Codes over GF(7)

Keisuke KODAIRA  Mihoko WADA  Tomoharu SHIBUYA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.11   pp.2247-2253
Publication Date: 2014/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.2247
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
amplitude damping,  quantum error correcting code,  asymmetric channel,  

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Summary: 
The amplitude damping (AD) quantum channel is one of the models describing evolution of quantum states. The construction of quantum error correcting codes for the AD channel based on classical codes has been presented, and Shor et al. proposed a class of classical codes over F3 which are efficiently applicable to this construction. In this study, we expand Shor's construction to that over F7, and succeeded to construct an AD code that has better parameters than AD codes constructed by Shor et al.