Details
| Original language | English |
|---|---|
| Article number | 042111 |
| Pages (from-to) | 04211 |
| Number of pages | 1 |
| Journal | J. Math. Phys |
| Volume | 55 |
| Issue number | 4 |
| Publication status | Published - 29 Apr 2014 |
Abstract
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by Heisenberg. Here we prove such relations for the case of two canonically conjugate observables like position and momentum, and establish a close connection with the more familiar preparation uncertainty relations constraining the sharpness of the distributions of the two observables in the same state. Both sets of relations are generalized to means of order α rather than the usual quadratic means, and we show that the optimal constants are the same for preparation and for measurement uncertainty. The constants are determined numerically and compared with some bounds in the literature. In both cases, the near-saturation of the inequalities entails that the state (resp. observable) is uniformly close to a minimizing one.
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: J. Math. Phys, Vol. 55, No. 4, 042111, 29.04.2014, p. 04211.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Measurement uncertainty relations
AU - Busch, P.
AU - Lahti, P.
AU - Werner, R. F.
N1 - Copyright: Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014/4/29
Y1 - 2014/4/29
N2 - Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by Heisenberg. Here we prove such relations for the case of two canonically conjugate observables like position and momentum, and establish a close connection with the more familiar preparation uncertainty relations constraining the sharpness of the distributions of the two observables in the same state. Both sets of relations are generalized to means of order α rather than the usual quadratic means, and we show that the optimal constants are the same for preparation and for measurement uncertainty. The constants are determined numerically and compared with some bounds in the literature. In both cases, the near-saturation of the inequalities entails that the state (resp. observable) is uniformly close to a minimizing one.
AB - Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by Heisenberg. Here we prove such relations for the case of two canonically conjugate observables like position and momentum, and establish a close connection with the more familiar preparation uncertainty relations constraining the sharpness of the distributions of the two observables in the same state. Both sets of relations are generalized to means of order α rather than the usual quadratic means, and we show that the optimal constants are the same for preparation and for measurement uncertainty. The constants are determined numerically and compared with some bounds in the literature. In both cases, the near-saturation of the inequalities entails that the state (resp. observable) is uniformly close to a minimizing one.
UR - http://www.scopus.com/inward/record.url?scp=84902257084&partnerID=8YFLogxK
U2 - 10.1063/1.4871444
DO - 10.1063/1.4871444
M3 - Article
VL - 55
SP - 04211
JO - J. Math. Phys
JF - J. Math. Phys
SN - 1089-7658
IS - 4
M1 - 042111
ER -