621 research outputs found
Point Estimation of States of Finite Quantum Systems
The estimation of the density matrix of a -level quantum system is studied
when the parametrization is given by the real and imaginary part of the entries
and they are estimated by independent measurements. It is established that the
properties of the estimation procedure depend very much on the invertibility of
the true state. In particular, in case of a pure state the estimation is less
efficient. Moreover, several estimation schemes are compared for the unknown
state of a qubit when one copy is measured at a time. It is shown that the
average mean quadratic error matrix is the smallest if the applied observables
are complementary. The results are illustrated by computer simulations.Comment: 16 pages, 5 figure
Covariance and Fisher information in quantum mechanics
Variance and Fisher information are ingredients of the Cramer-Rao inequality.
We regard Fisher information as a Riemannian metric on a quantum statistical
manifold and choose monotonicity under coarse graining as the fundamental
property of variance and Fisher information. In this approach we show that
there is a kind of dual one-to-one correspondence between the candidates of the
two concepts. We emphasis that Fisher informations are obtained from relative
entropies as contrast functions on the state space and argue that the scalar
curvature might be interpreted as an uncertainty density on a statistical
manifold.Comment: LATE
On Mutual Information in Multipartite Quantum States and Equality in Strong Subadditivity of Entropy
The challenge of equality in the strong subadditivity inequality of entropy
is approached via a general additivity of correlation information in terms of
nonoverlapping clusters of subsystems in multipartite states (density
operators). A family of tripartite states satisfying equality is derived.Comment: 8 pages; Latex2e and Revtex
Asymptotics of Quantum Relative Entropy From Representation Theoretical Viewpoint
In this paper it was proved that the quantum relative entropy can be asymptotically attained by Kullback Leibler divergences of
probabilities given by a certain sequence of POVMs. The sequence of POVMs
depends on , but is independent of the choice of .Comment: LaTeX2e. 8 pages. The title was changed from "Asymptotic Attainment
for Quantum Relative Entropy
Hamilton-Jacobi Theory and Information Geometry
Recently, a method to dynamically define a divergence function for a
given statistical manifold by means of the
Hamilton-Jacobi theory associated with a suitable Lagrangian function
on has been proposed. Here we will review this
construction and lay the basis for an inverse problem where we assume the
divergence function to be known and we look for a Lagrangian function
for which is a complete solution of the associated
Hamilton-Jacobi theory. To apply these ideas to quantum systems, we have to
replace probability distributions with probability amplitudes.Comment: 8 page
A new quantum version of f-divergence
This paper proposes and studies new quantum version of -divergences, a
class of convex functionals of a pair of probability distributions including
Kullback-Leibler divergence, Rnyi-type relative entropy and so on. There are
several quantum versions so far, including the one by Petz. We introduce
another quantum version (, below), defined as the
solution to an optimization problem, or the minimum classical - divergence
necessary to generate a given pair of quantum states. It turns out to be the
largest quantum -divergence. The closed formula of
is given either if is operator convex, or if one of the state is a pure
state. Also, concise representation of as a pointwise
supremum of linear functionals is given and used for the clarification of
various properties of the quality.
Using the closed formula of , we show: Suppose is
operator convex. Then the\ maximum - divergence of the probability
distributions of a measurement under the state and is strictly
less than . This statement
may seem intuitively trivial, but when is not operator convex, this is not
always true. A counter example is , which corresponds to total variation distance.
We mostly work on finite dimensional Hilbert space, but some results are
extended to infinite dimensional case.Comment: The proof of dual representation of the former version was misstated.
An alternative proof is presente
Mapping ecosystem functions and services in Eastern Europe using global-scale data sets
To assess future interactions between the environment and human well-being, spatially explicit ecosystem service models are needed. Currently available models mainly focus on provisioning services and do not distinguish changes in the functioning of the ecosystem (Ecosystem Functions – ESFs) and human use of such functions (Ecosystem Services – ESSs). This limits the insight on the impact of global change on human well-being. We present a set of models for assessing ESFs and ESSs. We mapped a diverse set of provisioning, regulating and cultural services, focusing on services that depend on the landscape structure. Services were mapped using global-scale data sets. We evaluated the models for a sample area comprising Eastern Europe. ESFs are mainly available in natural areas, while hotspots of ESS supply are found in areas with heterogeneous land cover. Here, natural land cover where ESFs are available is mixed with areas where the ESSs are utilized. We conclude that spatial patterns of several ESFs and ESSs can be mapped at global scale using existing global-scale data sets. As land-cover change has different impacts on different aspects of the interaction between humans and the environment, it is essential to clearly distinguish between ESFs and ESSs in integrated assessment studies
Quantum hypothesis testing with group symmetry
The asymptotic discrimination problem of two quantum states is studied in the
setting where measurements are required to be invariant under some symmetry
group of the system. We consider various asymptotic error exponents in
connection with the problems of the Chernoff bound, the Hoeffding bound and
Stein's lemma, and derive bounds on these quantities in terms of their
corresponding statistical distance measures. A special emphasis is put on the
comparison of the performances of group-invariant and unrestricted
measurements.Comment: 33 page
An entropic uncertainty principle for positive operator valued measures
Extending a recent result by Frank and Lieb, we show an entropic uncertainty
principle for mixed states in a Hilbert space relatively to pairs of positive
operator valued measures that are independent in some sense. This yields
spatial-spectral uncertainty principles and log-Sobolev inequalities for
invariant operators on homogeneous spaces, which are sharp in the compact case.Comment: 14 pages. v2: a technical assumption removed in main resul
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