Quantum Cryptography, Quantum Communication, and Quantum Computing in a Noisy Environment

  • Koji Nagata
  • Tadao Nakamura
  • Ahmed Farouk
Part of the Studies in Big Data book series (SBD, volume 33)


First, we study several information theories based on quantum computing in a desirable noiseless situation. (1) We present quantum key distribution based on Deutsch’s algorithm using an entangled state. (2) We discuss the fact that the Bernstein-Vazirani algorithm can be used for quantum communication including an error correction. Finally, we discuss the main results. We study the Bernstein-Vazirani algorithm in a noisy environment. The original algorithm determines a noiseless function. Here we consider the case that the function has an environmental noise. We introduce a noise term into the function f(x). So we have another noisy function g(x). The relation between them is \( g(x)=f(x)\pm O(\epsilon ). \) Here \(O(\epsilon )\ll 1\) is the noise term. The goal is to determine the noisy function g(x) with a success probability. The algorithm overcomes classical counterpart by a factor of N in a noisy environment.

PACS numbers

03.67.Lx (Quantum computation architectures and implementations) 03.67.Ac (Quantum algorithms protocols and simulations) 03.67.Dd (Quantum cryptography) 03.67.Hk (Quantum communication) 


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of PhysicsKorea Advanced Institute of Science and TechnologyDaejeonKorea
  2. 2.Department of Information and Computer ScienceKeio UniversityKohoku-kuJapan
  3. 3.Computer Sciences Department, Faculty of Computers and InformationMansoura UniversityMansouraEgypt

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