Investigation into the statistical nature of Bell’s inequalities

Investigation into the statistical nature of Bell’s inequalities The relationship between quantum statistics and classical probability theory is discussed. Meeting Bell’s inequalities is treated as reducing quantum measurements to classical probability distributions. The question of whether or not this is possible is given a mathematical formulation involving singular-value decomposition and the concept of quasi-probabilities. All the possible quasi-probability distributions are presented in compact form, and are shown not to be positive definite. The concept of a regularized solution that minimizes variance is introduced. An invariant is defined and discussed that provides an intuitive representation of Bell’s inequality and its violation. The method of quasi-probabilities and the density-matrix formalism are compared in the context of the tomographic description of quantum states. A statistical interpretation is given to Greenberger-Horne-Zeilinger states. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Russian Microelectronics Springer Journals

Investigation into the statistical nature of Bell’s inequalities

Loading next page...
 
/lp/springer_journal/investigation-into-the-statistical-nature-of-bell-s-inequalities-cC0ojZDo9h
Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2008 by MAIK Nauka
Subject
Engineering; Electrical Engineering
ISSN
1063-7397
eISSN
1608-3415
D.O.I.
10.1134/S1063739708050041
Publisher site
See Article on Publisher Site

Abstract

The relationship between quantum statistics and classical probability theory is discussed. Meeting Bell’s inequalities is treated as reducing quantum measurements to classical probability distributions. The question of whether or not this is possible is given a mathematical formulation involving singular-value decomposition and the concept of quasi-probabilities. All the possible quasi-probability distributions are presented in compact form, and are shown not to be positive definite. The concept of a regularized solution that minimizes variance is introduced. An invariant is defined and discussed that provides an intuitive representation of Bell’s inequality and its violation. The method of quasi-probabilities and the density-matrix formalism are compared in the context of the tomographic description of quantum states. A statistical interpretation is given to Greenberger-Horne-Zeilinger states.

Journal

Russian MicroelectronicsSpringer Journals

Published: Sep 21, 2008

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 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

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