arXiv:1403.4687quant-ph
Equivalence of wave-particle duality to entropic uncertainty
Abstract
Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behavior, yet that wave behavior disappears when one tries to determine the particle's path inside the interferometer. This idea has been formulated quantitively as an inequality, e.g., 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.
http://arxiv.org/pdf/1403.4687v2.pdf
nooberminView on HNParent context
http://arxiv.org/pdf/1403.4687v2.pdf is the actual preprint. I'm finding it pretty hard to parse. It seems to be a reformulation of what we already know about non-commuting observables in terms of entropy/ignorance. I might need to read some of the cited papers to understand…
ajkjkView on HNParent context
Here is the paper: http://arxiv.org/pdf/1403.4687v2.pdf My quick read suggests that the authors are restating the relationship using their "Entropic View" notation which, as it turns out, has the same expression if you come at it from the uncertainty principle side or the wave…
ChuckMcMView on HNParent context