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Quantum paradoxes, probability theory, and change of ensemble
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1082-8325
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: urn:nbn:se:liu:diva-38597Local ID: 44907ISBN: 91-7219-846-X (print)OAI: oai:DiVA.org:liu-38597DiVA: diva2:259446
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
List of papers
1. Bell’s inequality and detector inefficiency
Open this publication in new window or tab >>Bell’s inequality and detector inefficiency
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.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-87169 (URN)10.1103/PhysRevA.57.3304 (DOI)
Available from: 2013-01-11 Created: 2013-01-11 Last updated: 2017-12-06
2. Modeling the singlet state with local variables
Open this publication in new window or tab >>Modeling the singlet state with local variables
1999 (English)In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 256, no 4, 245-252 p.Article in journal (Refereed) Published
Abstract [en]

A local-variable model yielding the statistics from the singlet state is presented for the case of inefficient detectors and/or lowered visibility. It has independent errors and the highest efficiency at perfect visibility is 77.80%, while the highest visibility at perfect detector-efficiency is 63.66%. The model cannot be refuted by measurements made to date.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-38610 (URN)10.1016/S0375-9601(99)00236-4 (DOI)44987 (Local ID)44987 (Archive number)44987 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13
3. Necessary and sufficient detector-efficiency conditions for the Greenberger-Horne-Zeilinger paradox
Open this publication in new window or tab >>Necessary and sufficient detector-efficiency conditions for the Greenberger-Horne-Zeilinger paradox
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.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-38612 (URN)10.1103/PhysRevA.57.R3145 (DOI)44989 (Local ID)44989 (Archive number)44989 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13
4. Detector efficiency in the Greenberger-Horne-Zeilinger paradox: independent errors
Open this publication in new window or tab >>Detector efficiency in the Greenberger-Horne-Zeilinger paradox: independent errors
1999 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 59, no 6, 4801-4804 p.Article in journal (Refereed) Published
Abstract [en]

The Greenberger-Horne-Zeilinger (GHZ) paradox is subject to the detector-efficiency “loophole” in a similar manner as the Bell inequality. In a paper by J.-Å. Larsson [Phys. Rev. A 57, R3145 (1998)], the issue is investigated for very general assumptions. Here, the assumptions of constant efficiency and independent errors will be imposed, and it will be shown that the necessary and sufficient efficiency bound is not lowered, but remains at 75%. An explicit local-variable model is constructed in this paper to show the necessity of this bound. In other words, it is not possible to use the independence of experimental nondetection errors to rule out local realism in the GHZ paradox below 75% efficiency.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-38611 (URN)10.1103/PhysRevA.59.4801 (DOI)44988 (Local ID)44988 (Archive number)44988 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13
5. Two-photon Franson-type experiments and local realism
Open this publication in new window or tab >>Two-photon Franson-type experiments and local realism
1999 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 83, no 15, 2872-2876 p.Article in journal (Refereed) Published
Abstract [en]

The two-photon interferometric experiment proposed by J. D. Franson [Phys. Rev. Lett. 62, 2205 (1989)] is often treated as a “Bell test of local realism.” However, it has been suggested that this is incorrect due to the 50% postselection performed even in the ideal gedanken version of the experiment. Here we present a simple local hidden variable model of the experiment that successfully explains the results obtained in usual realizations of the experiment, even with perfect detectors. Furthermore, we also show that there is no such model if the switching of the local phase settings is done at a rate determined by the internal geometry of the interferometers.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-38609 (URN)10.1103/PhysRevLett.83.2872 (DOI)44986 (Local ID)44986 (Archive number)44986 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13
6. A possible unification of the Copenhagen and the Bohm interpretations using local realism
Open this publication in new window or tab >>A possible unification of the Copenhagen and the Bohm interpretations using local realism
2000 (English)In: Foundations of physics letters, ISSN 0894-9875, E-ISSN 1572-9524, Vol. 13, no 5, 477-486 p.Article in journal (Refereed) Published
Abstract [en]

It is well-known in the physics community that the Copenhagen interpretation of quantum mechanics is very different from the Bohm interpretation. Usually, a local realistic model is thought to be even further from these two, as in its purest form it cannot even yield the probabilities from quantum mechanics by the Bell theorem. Nevertheless, by utilizing the “efficiency loophole” such a model can mimic the quantum probabilities, and more importantly, in this paper it is shown that it is possible to interpret this latter kind of local realistic model such that it contains elements of reality as found in the Bohm interpretation, while retaining the complementarity present in the Copenhagen interpretation.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-38607 (URN)10.1023/A:1007884816456 (DOI)44945 (Local ID)44945 (Archive number)44945 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13

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