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Leung-Yan-Cheong, S. K. and Hellman, M.E. “Concerning a bound on undetected error probability,” IEEE Trans. Inf. Theory, vol. IT- 22. pp. 235-231, 1976.

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Article

Undetected Error Probability for Quantum Codes

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


American Journal of Applied Mathematics and Statistics. 2015, Vol. 3 No. 2, 76-79
DOI: 10.12691/ajams-3-2-6
Copyright © 2015 Science and Education Publishing

Cite this paper:
Manish Gupta, R.K. Narula, 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.

Correspondence to: Divya  Taneja, Yadavindra College of Engineering, Punjabi University Guru Kashi Campus, Talwandi Sabo, Punjab, India. Email: dtaneja25@yahoo.co.in

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.

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