Undetected Error Probability for Quantum Codes

Manish Gupta¹, R.K. Narula² and Divya Taneja^{3, 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

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

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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