Journal of Computer Technology & Applications

Journal of Computer Technology & Applications Review Article

Quantum Error Correction on Cryptography

  1. Sanjeev Patwa Department of Computer Science and Engineering, Mody University of Science and Technology, Lakshmangarh
  2. Tamanna Department of Computer Science and Engineering, Mody University of Science and Technology, Lakshmangarh
  3. Tejal Kumawat Department of Computer Science and Engineering, Mody University of Science and Technology, Lakshmangarh

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
  • cryptographic protocols
  • entropic uncertainty relations
  • noisy-storage cryptography
  • quantum data locking
  • quantum key distribution
  • quantum noisy-storage model
  • security
  • symmetric complementary bases
  • threshold code

References (10)

  1. Nadkarni PJ, Garani SS. Quantum error correction architecture for qudit stabilizer codes. Physical Review A. 2021;103(4). 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. 2020 IEEE International Symposium on Workload Characterization (IISWC). 2020:94-105. doi:10.1109/iiswc50251.2020.00018
  5. Broadbent A, Schaffner C. Quantum cryptography beyond quantum key distribution. Designs, Codes and Cryptography. 2015;78(1):351-382. doi:10.1007/s10623-015-0157-4
  6. K. J. H, Pal AK. Distinguishing phases via non-Markovian dynamics of entanglement in topological quantum codes under parallel magnetic field. Physical Review A. 2022;105(5). 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(2). doi:10.1103/physrevx.8.021054
  8. Linke NM, Gutierrez M, Landsman KA, Figgatt C, Debnath S, Brown KR, et al. Fault-tolerant quantum error detection. Science Advances. 2017;3(10). doi:10.1126/sciadv.1701074
  9. Fisher MPA, Khemani V, Nahum A, Vijay S. Random Quantum Circuits. Annual Review of Condensed Matter Physics. 2023;14(1):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. 2017;86(1):121-136. doi:10.1007/s10623-017-0330-z