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Complementarity and uncertainty in Mach-Zehnder interferometry and beyond

Busch, Paul and Shilladay, Christopher (2006) Complementarity and uncertainty in Mach-Zehnder interferometry and beyond. Physics Reports. pp. 1-31. ISSN 0370-1573

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Abstract

A coherent account of the connections and contrasts between the principles of complementarity and uncertainty is developed starting from a survey of the various formalizations of these principles. The conceptual analysis is illustrated by means of a set of experimental schemes based on Mach-Zehnder interferometry. In particular, path detection via entanglement with a probe system and (quantitative) quantum erasure are exhibited to constitute instances of joint unsharp, measurements of complementary pairs of physical quantities, path and interference observables. The analysis uses the representation of observables as positive-operator-valued measures (POVMs). The reconciliation of complementary experimental options in the sense of simultaneous unsharp preparations and measurements is expressed in terms of uncertainty relations of different kinds. The feature of complementarity, manifest in the present examples in the mutual exclusivity of path detection and interference observation, is recovered as a limit case from the appropriate uncertainty relation. It is noted that the complementarity and uncertainty principles are neither completely logically independent nor logical consequences of one another. Since entanglement is an instance of the uncertainty of quantum properties (of compound systems), it is moot to play out uncertainty and entanglement against each other as possible mechanisms enforcing complementarity. (c) 2006 Published by Elsevier B.V.

Item Type: Article
Copyright, Publisher and Additional Information: © 2006 Elsevier B.V. This is an author produced version of a paper published in Physics Reports. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: complementarity principle, uncertainty principle, joint measurement, Mach-Zehnder interferometer, path marking, erasure, QUANTUM-MECHANICAL DESCRIPTION, WAVE-PARTICLE DUALITY, JOINT MEASUREMENT, HIDDEN VARIABLES, PHYSICAL REALITY, OBSERVABLES, HEISENBERG, PRINCIPLE, MOMENTUM
Academic Units: The University of York > Mathematics (York)
Depositing User: Sherpa Assistant
Date Deposited: 31 Jan 2008 14:46
Last Modified: 17 Oct 2013 14:18
Published Version: http://dx.doi.org/10.1016/j.physrep.2006.09.001
Status: Published
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/3611

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