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Uncertainty from Heisenberg to Today
We explore the different meanings of "quantum uncertainty" contained in
Heisenberg's seminal paper from 1927, and also some of the precise definitions
that were explored later. We recount the controversy about "Anschaulichkeit",
visualizability of the theory, which Heisenberg claims to resolve. Moreover, we
consider Heisenberg's programme of operational analysis of concepts, in which
he sees himself as following Einstein. Heisenberg's work is marked by the
tensions between semiclassical arguments and the emerging modern quantum
theory, between intuition and rigour, and between shaky arguments and
overarching claims. Nevertheless, the main message can be taken into the new
quantum theory, and can be brought into the form of general theorems. They come
in two kinds, not distinguished by Heisenberg. These are, on one hand,
constraints on preparations, like the usual textbook uncertainty relation, and,
on the other, constraints on joint measurability, including trade-offs between
accuracy and disturbance.Comment: 36 pages, 1 figur
Heisenberg uncertainty for qubit measurements
Reports on experiments recently performed in Vienna [Erhard et al, Nature
Phys. 8, 185 (2012)] and Toronto [Rozema et al, Phys. Rev. Lett. 109, 100404
(2012)] include claims of a violation of Heisenberg's error-disturbance
relation. In contrast, we have presented and proven a Heisenberg-type relation
for joint measurements of position and momentum [Phys. Rev. Lett. 111, 160405
(2013)]. To resolve the apparent conflict, we formulate here a new general
trade-off relation for errors in qubit measurements, using the same concepts as
we did in the position-momentum case. We show that the combined errors in an
approximate joint measurement of a pair of +/-1 valued observables A,B are
tightly bounded from below by a quantity that measures the degree of
incompatibility of A and B. The claim of a violation of Heisenberg is shown to
fail as it is based on unsuitable measures of error and disturbance. Finally we
show how the experiments mentioned may directly be used to test our error
inequality.Comment: Version 3 contains further clarifications in our argument refuting
the alleged violation of Heisenberg's error-disturbance relation. Some new
material added on the connection between preparation uncertainty and
approximation error relation
Quantum sensing
"Quantum sensing" describes the use of a quantum system, quantum properties
or quantum phenomena to perform a measurement of a physical quantity.
Historical examples of quantum sensors include magnetometers based on
superconducting quantum interference devices and atomic vapors, or atomic
clocks. More recently, quantum sensing has become a distinct and rapidly
growing branch of research within the area of quantum science and technology,
with the most common platforms being spin qubits, trapped ions and flux qubits.
The field is expected to provide new opportunities - especially with regard to
high sensitivity and precision - in applied physics and other areas of science.
In this review, we provide an introduction to the basic principles, methods and
concepts of quantum sensing from the viewpoint of the interested
experimentalist.Comment: 45 pages, 13 figures. Submitted to Rev. Mod. Phy
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