Details
| Original language | English |
|---|---|
| Article number | 110305 |
| Pages (from-to) | 1-10 |
| Number of pages | 10 |
| Journal | Frontiers of physics |
| Volume | 11 |
| Issue number | 3 |
| Publication status | Published - 1 Apr 2016 |
Abstract
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by a Fourier transform. The physical examples discussed here are the standard position and momentum, number and angle, finite qudit systems, and strings of qubits for quantum information applications. The uncertainty relations allow for an arbitrary choice of metric for the outcome distance, and the choice of an exponent distinguishing, e.g., absolute and root mean square deviations. The emphasis of this article is on developing a unified treatment, in which one observable takes on values in an arbitrary locally compact Abelian group and the other in the dual group. In all cases, the phase space symmetry implies the equality of measurement and preparation uncertainty bounds. There is also a straightforward method for determining the optimal bounds.
Keywords
- measurement uncertainty, phase space, uncertainty relations
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: Frontiers of physics, Vol. 11, No. 3, 110305, 01.04.2016, p. 1-10.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Uncertainty relations for general phase spaces
AU - Werner, Reinhard F.
N1 - Publisher Copyright: © 2016, The Author(s). Copyright: Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by a Fourier transform. The physical examples discussed here are the standard position and momentum, number and angle, finite qudit systems, and strings of qubits for quantum information applications. The uncertainty relations allow for an arbitrary choice of metric for the outcome distance, and the choice of an exponent distinguishing, e.g., absolute and root mean square deviations. The emphasis of this article is on developing a unified treatment, in which one observable takes on values in an arbitrary locally compact Abelian group and the other in the dual group. In all cases, the phase space symmetry implies the equality of measurement and preparation uncertainty bounds. There is also a straightforward method for determining the optimal bounds.
AB - We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by a Fourier transform. The physical examples discussed here are the standard position and momentum, number and angle, finite qudit systems, and strings of qubits for quantum information applications. The uncertainty relations allow for an arbitrary choice of metric for the outcome distance, and the choice of an exponent distinguishing, e.g., absolute and root mean square deviations. The emphasis of this article is on developing a unified treatment, in which one observable takes on values in an arbitrary locally compact Abelian group and the other in the dual group. In all cases, the phase space symmetry implies the equality of measurement and preparation uncertainty bounds. There is also a straightforward method for determining the optimal bounds.
KW - measurement uncertainty
KW - phase space
KW - uncertainty relations
UR - http://www.scopus.com/inward/record.url?scp=84962448818&partnerID=8YFLogxK
U2 - 10.1007/s11467-016-0558-5
DO - 10.1007/s11467-016-0558-5
M3 - Article
VL - 11
SP - 1
EP - 10
JO - Frontiers of physics
JF - Frontiers of physics
SN - 2095-0462
IS - 3
M1 - 110305
ER -