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Necessary and sufficient detector-efficiency conditions for the Greenberger-Horne-Zeilinger paradox
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, R3145-R3149 p.Article in journal (Refereed) Published
Abstract [en]

In this paper detector efficiency conditions are derived for the Greenberger-Horne-Zeilinger (GHZ) paradox. The conditions will be necessary and sufficient, i.e., the GHZ paradox is explicable in terms of a local-variable model if the efficiency is below the bounds, and the GHZ prerequisites are inconsistent at higher efficiencies. The derivation does not make use of any of the symmetry assumptions usually made in the literature, most notably the assumption of independent errors. The errors in local-hidden-variable models are governed by the “hidden variable” and, therefore, one cannot in general assume that the errors are independent. It will be shown that this assumption is not necessary. Moreover, bounds are presented that do not need the emission rate of particle triples to be known. An example of such a bound is the ratio of the triple coincidence rate and the double coincidence rate at two detectors, which needs to be higher than 75% to yield a contradiction.

Place, publisher, year, edition, pages
1998. Vol. 57, no 5, R3145-R3149 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-38612DOI: 10.1103/PhysRevA.57.R3145Local ID: 44989OAI: oai:DiVA.org:liu-38612DiVA: diva2:259461
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2016-08-31
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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