Quantum walk in terms of quantum Bernoulli noises

Quantum walk in terms of quantum Bernoulli noises Quantum Bernoulli noises are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation in equal time. In this paper, we first present some new results concerning quantum Bernoulli noises, which themselves are interesting. Then, based on these new results, we construct a time-dependent quantum walk with infinitely many degrees of freedom. We prove that the walk has a unitary representation and hence belongs to the category of the so-called unitary quantum walks. We examine its distribution property at the vacuum initial state and some other initial states and find that it has the same limit distribution as the classical random walk, which contrasts sharply with the case of the usual quantum walks with finite degrees of freedom. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum walk in terms of quantum Bernoulli noises

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1259-2
Publisher site
See Article on Publisher Site

Abstract

Quantum Bernoulli noises are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation in equal time. In this paper, we first present some new results concerning quantum Bernoulli noises, which themselves are interesting. Then, based on these new results, we construct a time-dependent quantum walk with infinitely many degrees of freedom. We prove that the walk has a unitary representation and hence belongs to the category of the so-called unitary quantum walks. We examine its distribution property at the vacuum initial state and some other initial states and find that it has the same limit distribution as the classical random walk, which contrasts sharply with the case of the usual quantum walks with finite degrees of freedom.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 11, 2016

References

  • Limit measure of inhomogeneous discrete-time quantum walks in one dimension
    Konno, N; Luczak, T; Segawa, E

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