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Sharp uncertainty relations for number and angle

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JournalJournal of Mathematical Physics
DateSubmitted - Jan 2018
DateAccepted/In press - 18 Mar 2018
DateE-pub ahead of print - 5 Apr 2018
DatePublished (current) - Apr 2018
Issue number4
Number of pages16
Early online date5/04/18
Original languageEnglish


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.

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    Research areas

  • quantum mechanics, uncertainty relations

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