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

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 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.