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

**Authors:** Koji Nagata, Tadao Nakamura

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

**Download:** **PDF**

### Submission history

[v1] 2017-04-03 01:19:04

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