Details
| Original language | English |
|---|---|
| Article number | 1261 |
| Pages (from-to) | 1261-1281 |
| Number of pages | 21 |
| Journal | Rev. Mod. Phys. |
| Volume | 86 |
| Issue number | 4 |
| Publication status | Published - 18 Dec 2014 |
Abstract
Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation. Here the conflict is resolved by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics. Two approaches to adapting the classic notion of root-mean-square error to quantum measurements are discussed. One is based on the concept of a noise operator; its natural operational content is that of a mean deviation of the values of two observables measured jointly, and thus its applicability is limited to cases where such joint measurements are available. The second error measure quantifies the differences between two probability distributions obtained in separate runs of measurements and is of unrestricted applicability. We show that there are no nontrivial unconditional joint-measurement bounds for state-dependent errors in the conceptual framework discussed here, while Heisenberg-type measurement uncertainty relations for state-independent errors have been proven.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Rev. Mod. Phys., Vol. 86, No. 4, 1261, 18.12.2014, p. 1261-1281.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Colloquium
T2 - Quantum root-mean-square error and measurement uncertainty relations
AU - Busch, P.
AU - Lahti, P.
AU - Werner, R. F.
N1 - Publisher Copyright: © 2014 American Physical Society. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2014/12/18
Y1 - 2014/12/18
N2 - Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation. Here the conflict is resolved by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics. Two approaches to adapting the classic notion of root-mean-square error to quantum measurements are discussed. One is based on the concept of a noise operator; its natural operational content is that of a mean deviation of the values of two observables measured jointly, and thus its applicability is limited to cases where such joint measurements are available. The second error measure quantifies the differences between two probability distributions obtained in separate runs of measurements and is of unrestricted applicability. We show that there are no nontrivial unconditional joint-measurement bounds for state-dependent errors in the conceptual framework discussed here, while Heisenberg-type measurement uncertainty relations for state-independent errors have been proven.
AB - Recent years have witnessed a controversy over Heisenberg's famous error-disturbance relation. Here the conflict is resolved by way of an analysis of the possible conceptualizations of measurement error and disturbance in quantum mechanics. Two approaches to adapting the classic notion of root-mean-square error to quantum measurements are discussed. One is based on the concept of a noise operator; its natural operational content is that of a mean deviation of the values of two observables measured jointly, and thus its applicability is limited to cases where such joint measurements are available. The second error measure quantifies the differences between two probability distributions obtained in separate runs of measurements and is of unrestricted applicability. We show that there are no nontrivial unconditional joint-measurement bounds for state-dependent errors in the conceptual framework discussed here, while Heisenberg-type measurement uncertainty relations for state-independent errors have been proven.
UR - http://www.scopus.com/inward/record.url?scp=84919933384&partnerID=8YFLogxK
U2 - 10.1103/RevModPhys.86.1261
DO - 10.1103/RevModPhys.86.1261
M3 - Article
VL - 86
SP - 1261
EP - 1281
JO - Rev. Mod. Phys.
JF - Rev. Mod. Phys.
SN - 1539-0756
IS - 4
M1 - 1261
ER -