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

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Abstract

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 result. 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) ± O(𝜖). Here O(𝜖) ≪ 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.

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Authors and Affiliations

  1. Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Korea

    Koji Nagata

  2. Department of Information and Computer Science, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

    Tadao Nakamura

Authors
  1. Koji Nagata
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  2. Tadao Nakamura
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Correspondence to Koji Nagata.

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Nagata, K., Nakamura, T. Quantum Cryptography, Quantum Communication, and Quantum Computer in a Noisy Environment. Int J Theor Phys 56, 2086–2100 (2017). https://doi.org/10.1007/s10773-017-3352-4

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  • DOI: https://doi.org/10.1007/s10773-017-3352-4

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