Equivalence of wave–particle duality to entropic uncertainty

Patrick J. Coles (), Jedrzej Kaniewski and Stephanie Wehner
Additional contact information
Patrick J. Coles: Centre for Quantum Technologies, National University of Singapore
Jedrzej Kaniewski: Centre for Quantum Technologies, National University of Singapore
Stephanie Wehner: Centre for Quantum Technologies, National University of Singapore

Nature Communications, 2014, vol. 5, issue 1, 1-8

Abstract: Abstract Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behaviour, yet that wave behaviour disappears when one tries to determine the particle’s path inside the interferometer. This idea has been formulated quantitatively as an inequality, for example, by Englert and Jaeger, Shimony and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave–particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg’s uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely, the min- and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models. As an illustration, we derive a novel relation that captures the coherence in a quantum beam splitter.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.nature.com/articles/ncomms6814 Abstract (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:5:y:2014:i:1:d:10.1038_ncomms6814

Ordering information: This journal article can be ordered from
https://www.nature.com/ncomms/

DOI: 10.1038/ncomms6814

Access Statistics for this article

Nature Communications is currently edited by Nathalie Le Bot, Enda Bergin and Fiona Gillespie

More articles in Nature Communications from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().