Details
| Original language | English |
|---|---|
| Article number | 042102 |
| Number of pages | 1 |
| Journal | Journal of Mathematical Physics |
| Volume | 59 |
| Issue number | 4 |
| Early online date | 5 Apr 2018 |
| Publication status | Published - Apr 2018 |
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of Mathematical Physics, Vol. 59, No. 4, 042102, 04.2018.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Sharp uncertainty relations for number and angle
AU - Busch, P.
AU - Kiukas, J.
AU - Werner, R. F.
N1 - Funding information: R.F.W. acknowledges funding by the DFG through the research training group RTG 1991. J.K. acknowledges funding from the EPSRC Project Nos. EP/J009776/1 and EP/M01634X/1. We thank Joe Renes for suggesting also the discrete metric on Z, and Rainer Hempel for helpful communications concerning the variational principle in Sec. VII. R.F.W. acknowledges funding by the DFG through the research training group RTG 1991. J.K. acknowledges funding from the EPSRC Project Nos. EP/J009776/1 and EP/M01634X/1.
PY - 2018/4
Y1 - 2018/4
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85045309780&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1604.00566
DO - 10.48550/arXiv.1604.00566
M3 - Article
VL - 59
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 4
M1 - 042102
ER -