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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 language  English 

Article number  042102 
Journal  Journal of Mathematical Physics 
Volume  59 
Issue number  4 
DOIs  
Publication status  Published  05 Apr 2018 
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Dive into the research topics of 'Sharp uncertainty relations for number and angle'. Together they form a unique fingerprint.Projects
 1 Finished

Control characterisation of noisy quantum devices
Engineering and Physical Sciences Research Council
01 Jun 2015 → 30 Sept 2016
Project: Externally funded research