American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: http://www.sciepub.com/journal/ajams Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2015, 3(2), 76-79
DOI: 10.12691/ajams-3-2-6
Open AccessArticle

Undetected Error Probability for Quantum Codes

Manish Gupta1, R.K. Narula2 and Divya Taneja3, 4,

1Baba Farid College of Engineering & Technology Bathinda, Punjab, India

2PIT, Mansa, Punjab, India

3Yadavindra College of Engineering, Punjabi University Guru Kashi Campus, Talwandi Sabo, Punjab, India

4Research Scholar Punjab Technical University, Jalandhar, Punjab, India

Pub. Date: April 15, 2015

Cite this paper:
Manish Gupta, R.K. Narula and Divya Taneja. Undetected Error Probability for Quantum Codes. American Journal of Applied Mathematics and Statistics. 2015; 3(2):76-79. doi: 10.12691/ajams-3-2-6

Abstract

From last fourteen years the work on undetected error probability for quantum codes has been silent. The undetected error probability has been discussed by Ashikhmin [3] in which it was proved that the average probability of undetected error for a given code is essentially given by a function of its weight enumerators. In this paper, new upper bounds on undetected error probability for quantum codes used for error detection on depolarization channel are given. It has also been established that the probability of undetected errors for quantum codes over depolarization channel do satisfy the upper bound analogous to classical codes.

Keywords:
additive codes stabilizer pure and impure codes weight enumerator probability of undetected error

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