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Bell’s inequality and detector inefficiency
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1082-8325
1998 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 57, no 5, 3304-3308 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, a method of generalizing the Bell inequality is presented that makes it possible to include detector inefficiency directly in the original Bell inequality. To enable this, the concept of “change of ensemble” will be presented, providing both qualitative and quantitative information on the nature of the “loophole” in the proof of the original Bell inequality. In a local hidden-variable model lacking change of ensemble, the generalized inequality reduces to an inequality that quantum mechanics violates as strongly as the original Bell inequality, irrespective of the level of efficiency of the detectors. A model that contains change of ensemble lowers the violation, and a bound for the level of change is obtained. The derivation of the bound in this paper is not dependent upon any symmetry assumptions such as constant efficiency, or even the assumption of independent errors.

Place, publisher, year, edition, pages
1998. Vol. 57, no 5, 3304-3308 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-87169DOI: 10.1103/PhysRevA.57.3304OAI: oai:DiVA.org:liu-87169DiVA: diva2:586507
Available from: 2013-01-11 Created: 2013-01-11 Last updated: 2017-12-06
In thesis
1. Quantum paradoxes, probability theory, and change of ensemble
Open this publication in new window or tab >>Quantum paradoxes, probability theory, and change of ensemble
2000 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, the question "What kind of models can be used to describe microcosmos?" will be discussed. Being difficult and very large in scope, the question has here been restricted to whether or not Local Realistic models can be used to describe Quantum-Mechanical processes, one of a collection of questions often referred to as Quantum Paradoxes. Two such paradoxes will be investigated using techniques from probability theory: the Bell inequality and the Greenberger-Horne-Zeilinger (GHZ) paradox.

A problem with the two mentioned paradoxes is that they are only valid when the detectors are 100% efficient, whereas present experimental efficiency is much lower than that. Here, an approach is presented which enables a generalization of both the Bell inequality and the GHZ paradox to the inefficient case. This is done by introducing the concept of change of ensemble, which provides both qualitative and quantitative information on the nature of the "loophole" in the 100% efficiency prerequisite, and is more fundamental in this regard than the efficiency concept. Efficiency estimates are presented which are easy to obtain from experimental coincidence data, and a connection is established between these estimates and the concept of change of ensemble.

The concept is also studied in the context of Franson interferometry, where the Bell inequality cannot immediately be used. Unexpected subtleties occur when trying to establish whether or not a Local Realistic model of the data is possible even in the ideal case. A Local Realistic model of the experiment is presented, but nevertheless, by introducing an additional requirement on the experimental setup it is possible to refute the mentioned model and show that no other Local Realistic model exists.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2000. 92 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 654
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-38597 (URN)44907 (Local ID)91-7219-846-X (ISBN)44907 (Archive number)44907 (OAI)
Public defence
2000-11-10, Hörsal Planck, Fysikhuset, Linköpings Universitet, Linköping, 13:15 (Swedish)
Opponent
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2016-08-31

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Larsson, Jan-Åke

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