Sharp uncertainty relations for number and angle

Paul Busch, Jukka Kiukas, R. F. Werner

Research output: Contribution to journalArticlepeer-review

4 Citations (SciVal)
141 Downloads (Pure)


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
JournalJournal of Mathematical Physics
Issue number4
Publication statusPublished - 05 Apr 2018


Dive into the research topics of 'Sharp uncertainty relations for number and angle'. Together they form a unique fingerprint.

Cite this