47 research outputs found
Covariant observables on a nonunimodular group
It is shown that the characterization of covariant positive operator measures
on nonunimodular locally compact groups can be obtained by using vector measure
theoretic methods, without an application of Mackey's imprimitivity theorem.Comment: 13 pages, to be published in Journal of Mathematical Analysis and
Application
A note on the measurement of phase space observables with an eight-port homodyne detector
It is well known that the Husimi Q-function of the signal field can actually
be measured by the eight-port homodyne detection technique, provided that the
reference beam (used for homodyne detection) is a very strong coherent field so
that it can be treated classically. Using recent rigorous results on the
quantum theory of homodyne detection observables, we show that any phase space
observable, and not only the Q-function, can be obtained as a high amplitude
limit of the signal observable actually measured by an eight-port homodyne
detector. The proof of this fact does not involve any classicality assumption.Comment: 8 pages, 1 figur
A note on infinite extreme correlation matrices
We give a characterization for the extreme points of the convex set of
correlation matrices with a countable index set. A Hermitian matrix is called a
correlation matrix if it is positive semidefinite with unit diagonal entries.
Using the characterization we show that there exist extreme points of any rank.Comment: 7 page
On the notion of coexistence in quantum mechanics
The notion of coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review examples illustrating the necessary degrees of unsharpness for two noncommuting observables to be jointly measurable (in one sense of the phrase). We demonstrate the possibility of measuring together (in another sense of the phrase) noncoexistent observables. This leads us to a reconsideration of the connection between joint measurability and noncommutativity of observables and of the statistical and individual aspects of quantum measurements
Continuous variable tomographic measurements
Using a recent result of Albini et al. to represent quantum homodyne
tomography in terms of a single observable (as a normalized positive operator
measure) we construct a generalized Markov kernel which transforms (the
measurement outcome statistics of) this observable into (the measurement
outcome statistics of) a covariant phase space observable. We also consider the
inverse question. Finally, we add some remarks on the quantum theoretical
justification of the experimental implementations of these observables in terms
of balanced homodyne and 8-port detection techniques, respectively.Comment: 9 page
Quantum tomography, phase space observables, and generalized Markov kernels
We construct a generalized Markov kernel which transforms the observable
associated with the homodyne tomography into a covariant phase space observable
with a regular kernel state. Illustrative examples are given in the cases of a
'Schrodinger cat' kernel state and the Cahill-Glauber s-parametrized
distributions. Also we consider an example of a kernel state when the
generalized Markov kernel cannot be constructed.Comment: 20 pages, 3 figure