Quantum Error Correction on Cryptography

Year : 2024 | Volume :15 | Issue : 01 | Page : 18-23
By

    Sanjeev Patwa

  1. Tamanna

  2. Tejal Kumawat

  1. Associate Professor, Department of Computer Science and Engineering, Mody University of Science and Technology, Lakshmangarh, Rajasthan, India
  2. Student, Department of Computer Science and Engineering, Mody University of Science and Technology, Lakshmangarh, Rajasthan, India
  3. Student, Department of Computer Science and Engineering, Mody University of Science and Technology, Lakshmangarh, Rajasthan, India

Abstract

This article introduces novel concepts in quantum error correction and cryptography. It explores “approximate quantum error correction” (AQEC), which relaxes the requirement for perfect error correction in quantum systems. AQEC specializes in creating codes tailored to specific types of noise models. The study establishes a universal, near-optimal recovery map for AQEC, simplifying the identification of effective approximate codes. In the realm of noisy-storage cryptography, the research envisions secure two-party cryptographic protocols in the presence of noisy and bounded quantum storage devices. These protocols remain secure, even when a dishonest party can store most information with a noiseless quantum memory, pushing the limits of quantum noisy-storage models. Furthermore, the research explores entropic uncertainty relations involving symmetric complementary bases, a critical aspect in assessing the security of quantum cryptographic protocols. It introduces sets of symmetric, complementary bases, offering new lower bounds for uncertainty relations, with precise bounds for specific cases. Furthermore, the research explores the integration of error correction and authentication in quantum cryptography, proposing the “threshold code.” This code efficiently combines error correction and authentication, offering enhanced security and practicality in quantum communication.

Keywords: Quantum error correction, approximate quantum error correction, noisy-storage cryptography, entropic uncertainty relations, symmetric complementary bases, quantum data locking, cryptographic protocols, threshold code, quantum key distribution, security, quantum noisy-storage model

[This article belongs to Journal of Computer Technology & Applications(jocta)]

How to cite this article: Sanjeev Patwa, Tamanna, Tejal Kumawat.Quantum Error Correction on Cryptography.Journal of Computer Technology & Applications.2024; 15(01):18-23.
How to cite this URL: Sanjeev Patwa, Tamanna, Tejal Kumawat , Quantum Error Correction on Cryptography jocta 2024 {cited 2024 Apr 05};15:18-23. Available from: https://journals.stmjournals.com/jocta/article=2024/view=140172


References

  1. Nadkarni PJ, Garani SS. Quantum error correction architecture for qudit stabilizer codes. Physical Review. Part A. 2021;103:042420. doi: 10.1103/PhysRevA.103.042420.
  2. Nielsen MA, Chuang IL. Quantum Computation and Quantum Information. Cambridge, UK: Cambridge University Press; 2010.
  3. Saki AA, Alam M, Ghosh S. Study of Decoherence in Quantum Computers: A Circuit-Design Perspective. arXiv Preprint ArXiv:1904.04323. 2019 Apr 8.
  4. Liu J, Zhou H. Reliability Modeling of NISQ- Era Quantum Computers. IEEE international symposium on workload characterization (IISWC). 2020. pp. 94–105. doi: 10.1109/IISWC50251.2020.00018.
  5. Broadbent A, Schaffner C. Quantum cryptography beyond quantum key distribution. Designs, Codes, and Cryptography. 2016;78:351–382. doi: 10.1007/s10623-015-0157-4. PubMed: 32226229.
  6. Pal AK, Pal AK. Distinguishing phases via non-Markovian dynamics of entanglement in topological quantum codes under parallel magnetic field. Physical Review. Part A. 2022;105:052421. doi: 10.1103/PhysRevA.105.052421.
  7. Fukui K, Tomita A, Okamoto A, Fujii K. High-threshold fault-tolerant quantum computation with analog quantum error correction. Physical Review X. 2018;8:021054. doi: 10.1103/PhysRevX.8.021054.
  8. Linke NM, Gutierrez M, Landsman KA, Figgatt C, Debnath S, Brown KR, Monroe C. Fault-tolerant quantum error detection. Science Advances. 2017;3:e1701074. doi: 10.1126/sciadv.1701074. PubMed: 29062889.
  9. Fisher MPA, Khemani V, Nahum A, Vijay S. Random quantum circuits. Annual Review of Condensed Matter Physics. 2023;14:335–379. doi: 10.1146/annurev-conmatphys-031720-030658.
  10. Guenda K, Jitman S, Gulliver TA. Constructions of good entanglement-assisted quantum error correcting codes. Designs, Codes and Cryptography. 2018;86:121–136. doi: 10.1007/s10623-017-0330-z.
Regular Issue Subscription Review Article
Volume 15
Issue 01
Received November 24, 2023
Accepted December 13, 2023
Published April 5, 2024
Views: 45