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)\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.
Comments: 9 Pages. International Journal of Theoretical Physics, (2017), DOI 10.1007/s10773-017-3352-4
[v1] 2017-04-03 01:19:04
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