Sharp uncertainty relations for number and angle

Paul Busch, Jukka Kiukas, Reinhard F Werner

Research output: Contribution to journalArticlepeer-review

Abstract

We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the problem in either variable implies that measurement uncertainty and preparation uncertainty coincide quantitatively, and the bounds depend only on the choice of two metrics used to quantify the difference of number and angle outputs, respectively. For each type of observable, we discuss two natural choices of metric and discuss the resulting optimal bounds with both numerical and analytical methods. We also develop some simple and explicit (albeit not sharp) lower bounds, using an apparently new method for obtaining certified lower bounds to ground state problems.
Original languageEnglish
Article number042102
Number of pages16
JournalJournal of Mathematical Physics
Volume59
Issue number4
Early online date5 Apr 2018
DOIs
Publication statusPublished - Apr 2018

Bibliographical note

Published by AIP Publishing. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

Keywords

  • quantum mechanics
  • uncertainty relations

Cite this