The stationary measure of a space-inhomogeneous three-state quantum walk on the line

The stationary measure of a space-inhomogeneous three-state quantum walk on the line Three-state quantum walks are quite different from two-state quantum walks. Following Endo and Konno (2013), one natural question is: What is the stationary measure of a space-inhomogeneous three-state quantum walk? In this paper, we consider a special space-inhomogeneous three-state quantum walk on the line, which we call the three-state Wojcik walk. We calculate its eigenvalues. And by using the SGF method introduced by Konno et al. (Quantum Inf Pocess 12:35–53, 2013), we obtain its stationary measure. We find that the measure decays exponentially with respect to position under some mild conditions; however, if the walk takes $$-1$$ - 1 as its eigenvalue, the asymptotic behavior of the measure is independent of position, which contrasts sharply with that of two-state quantum walks. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

The stationary measure of a space-inhomogeneous three-state quantum walk on the line

Loading next page...
 
/lp/springer_journal/the-stationary-measure-of-a-space-inhomogeneous-three-state-quantum-tMHFYGYJN6
Publisher
Springer US
Copyright
Copyright © 2015 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/s11128-015-0922-3
Publisher site
See Article on Publisher Site

Abstract

Three-state quantum walks are quite different from two-state quantum walks. Following Endo and Konno (2013), one natural question is: What is the stationary measure of a space-inhomogeneous three-state quantum walk? In this paper, we consider a special space-inhomogeneous three-state quantum walk on the line, which we call the three-state Wojcik walk. We calculate its eigenvalues. And by using the SGF method introduced by Konno et al. (Quantum Inf Pocess 12:35–53, 2013), we obtain its stationary measure. We find that the measure decays exponentially with respect to position under some mild conditions; however, if the walk takes $$-1$$ - 1 as its eigenvalue, the asymptotic behavior of the measure is independent of position, which contrasts sharply with that of two-state quantum walks.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jan 21, 2015

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from Google Scholar, PubMed
Create lists to organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off