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Title: Quantum stabilizer codes for correlated and asymmetric depolarizing errors

Abstract

We study the performance of common quantum stabilizer codes in the presence of asymmetric and correlated errors. Specifically, we consider the depolarizing noisy quantum memory channel and perform quantum error correction via the five- and seven-qubit stabilizer codes. We characterize these codes by means of the entanglement fidelity as a function of the error probability and the degree of memory. We show that their performances are lowered by the presence of correlations, and we compute the error probability threshold values for code effectiveness. Furthermore, we uncover that the asymmetry in the error probabilities does not affect the performance of the five-qubit code, while it does affect the performance of the seven-qubit code, which results in being less effective when considering correlated and symmetric depolarizing errors but more effective for correlated and asymmetric errors.

Authors:
;  [1]
  1. School of Science and Technology, Physics Division, University of Camerino, I-62032 Camerino (Italy)
Publication Date:
OSTI Identifier:
21440475
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 82; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.82.012306; (c) 2010 The American Physical Society; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMMETRY; CORRECTIONS; CORRELATIONS; ERRORS; PERFORMANCE; PROBABILITY; QUANTUM CRYPTOGRAPHY; QUANTUM ENTANGLEMENT; QUANTUM STATES; SECRECY PROTECTION; SYMMETRY; CRYPTOGRAPHY

Citation Formats

Cafaro, Carlo, and Mancini, Stefano. Quantum stabilizer codes for correlated and asymmetric depolarizing errors. United States: N. p., 2010. Web. doi:10.1103/PHYSREVA.82.012306.
Cafaro, Carlo, & Mancini, Stefano. Quantum stabilizer codes for correlated and asymmetric depolarizing errors. United States. https://doi.org/10.1103/PHYSREVA.82.012306
Cafaro, Carlo, and Mancini, Stefano. 2010. "Quantum stabilizer codes for correlated and asymmetric depolarizing errors". United States. https://doi.org/10.1103/PHYSREVA.82.012306.
@article{osti_21440475,
title = {Quantum stabilizer codes for correlated and asymmetric depolarizing errors},
author = {Cafaro, Carlo and Mancini, Stefano},
abstractNote = {We study the performance of common quantum stabilizer codes in the presence of asymmetric and correlated errors. Specifically, we consider the depolarizing noisy quantum memory channel and perform quantum error correction via the five- and seven-qubit stabilizer codes. We characterize these codes by means of the entanglement fidelity as a function of the error probability and the degree of memory. We show that their performances are lowered by the presence of correlations, and we compute the error probability threshold values for code effectiveness. Furthermore, we uncover that the asymmetry in the error probabilities does not affect the performance of the five-qubit code, while it does affect the performance of the seven-qubit code, which results in being less effective when considering correlated and symmetric depolarizing errors but more effective for correlated and asymmetric errors.},
doi = {10.1103/PHYSREVA.82.012306},
url = {https://www.osti.gov/biblio/21440475}, journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 82,
place = {United States},
year = {Thu Jul 15 00:00:00 EDT 2010},
month = {Thu Jul 15 00:00:00 EDT 2010}
}