Research output: Contribution to journal › Article

**Sharp uncertainty relations for number and angle.** / Busch, Paul; Kiukas, Jukka; Werner, Reinhard F.

Research output: Contribution to journal › Article

Busch, P, Kiukas, J & Werner, RF 2018, 'Sharp uncertainty relations for number and angle', *Journal of Mathematical Physics*, vol. 59, no. 4, 042102. https://doi.org/10.1063/1.5030101

Busch, P., Kiukas, J., & Werner, R. F. (2018). Sharp uncertainty relations for number and angle. *Journal of Mathematical Physics*, *59*(4), [042102]. https://doi.org/10.1063/1.5030101

Busch P, Kiukas J, Werner RF. Sharp uncertainty relations for number and angle. Journal of Mathematical Physics. 2018 Apr;59(4). 042102. https://doi.org/10.1063/1.5030101

@article{04de63d5c242437a8a64032346958471,

title = "Sharp uncertainty relations for number and angle",

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.",

keywords = "quantum mechanics, uncertainty relations",

author = "Paul Busch and Jukka Kiukas and Werner, {Reinhard F}",

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",

year = "2018",

month = "4",

doi = "10.1063/1.5030101",

language = "English",

volume = "59",

journal = "J. Math. Phys.",

issn = "0022-2488",

publisher = "American Institute of Physics Publising LLC",

number = "4",

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TY - JOUR

T1 - Sharp uncertainty relations for number and angle

AU - Busch, Paul

AU - Kiukas, Jukka

AU - Werner, Reinhard F

N1 - 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

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.

KW - quantum mechanics

KW - uncertainty relations

UR - https://arxiv.org/abs/1604.00566

U2 - 10.1063/1.5030101

DO - 10.1063/1.5030101

M3 - Article

VL - 59

JO - J. Math. Phys.

JF - J. Math. Phys.

SN - 0022-2488

IS - 4

M1 - 042102

ER -