Complementarity and uncertainty in quantum interference

Shilladay, Christopher Robin

Abstract

This thesis is concerned with the notions of complementarity and uncertainty encountered in quantum mechanics. Its starting point is an assessment of how these concepts have been represented and illustrated by various writers dating back to their inception. Following the survey a coherent account of the connections and contrasts between complementarity and uncertainty is developed in the context of Mach-Zehnder interferometry. The effect on the interference pattern contrast of path detection via entanglement with a probe system, is explored and a joint unsharp measurement scheme of the complementary pairs, path and interference, described. The Mach-Zehnder set-up proves sufficiently versatile to show that quantum erasure and quantitative quantum erasure constitute instances of joint unsharp measurement of complementary observables. The analysis uses the representation of observables as positive operator valued measures.

Path detection and interference observation require different experimental set-ups but can be reconciled in the simultaneous unsharp measurement and preparation. This reconciliation is expressed as an uncertainty relation however the mutually exclusive feature of complementarity is not discarded. It is possible to recover strict complementarity as a limit case of the appropriate uncertainty relation.

One motivation for this study is the effort some authors have made in trying to express the founding features of quantum mechanics in the form of a hierarchy of significance. Here it is shown that complementarity and uncertainty have separate identities but are not completely independent of each other. Consequently, establishing a hierarchy of these features within the present formalism of quantum mechanics is not possible.

Citation

Shilladay, C. R. Complementarity and uncertainty in quantum interference. (Thesis). University of Hull. https://hull-repository.worktribe.com/output/4208409

• Thesis Type: Thesis
• Deposit Date: Aug 15, 2011
• Publicly Available Date: Feb 22, 2023
• Keywords: Mathematics (Applied); Physics; Quantum theory
• Public URL: https://hull-repository.worktribe.com/output/4208409
• Additional Information: , The University of Hull
• Award Date: Oct 1, 2007