426 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
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 â ESFs) and human use of such functions (Ecosystem Services â 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
Mapping and modelling the effects of land use and land management change on ecosystem services from local ecosystems and landscapes to global biomes
Herstel en duurzaam beheer van biodiversiteit en ecosysteemdiensten worden steeds meer geĂŻntegreerd in nationaal en internationaal beleid. In dit proefschrift wordt een methodologie ontwikkeld voor de kwantificering van effecten van landmanagement op de ruimtelijke verspreiding van ecosysteemdiensten, zodat de door landmanagement veroorzaakte trade-offs tussen ecosysteemdiensten bepaald kunnen worden voor zowel lokale ecosystemen en landschappen als regionale en mondiale biomen. Een groot aantal ecosysteemdiensten zijn bestudeerd. De karterings- en modelleringsmethoden zijn toegepast en gecombineerd met scenario-analyse in de Nederlandse en Zuid-Afrikaanse studies. Voor Nederland is het landschap van Het Groene Woud bestudeerd
Continuity and Stability of Partial Entropic Sums
Extensions of Fannes' inequality with partial sums of the Tsallis entropy are
obtained for both the classical and quantum cases. The definition of kth
partial sum under the prescribed order of terms is given. Basic properties of
introduced entropic measures and some applications are discussed. The derived
estimates provide a complete characterization of the continuity and stability
properties in the refined scale. The results are also reformulated in terms of
Uhlmann's partial fidelities.Comment: 9 pages, no figures. Some explanatory and technical improvements are
made. The bibliography is extended. Detected errors and typos are correcte
Additivity and multiplicativity properties of some Gaussian channels for Gaussian inputs
We prove multiplicativity of maximal output norm of classical noise
channels and thermal noise channels of arbitrary modes for all under the
assumption that the input signal states are Gaussian states. As a direct
consequence, we also show the additivity of the minimal output entropy and that
of the energy-constrained Holevo capacity for those Gaussian channels under
Gaussian inputs. To the best of our knowledge, newly discovered majorization
relation on symplectic eigenvalues, which is also of independent interest,
plays a central role in the proof.Comment: 9 pages, no figures. Published Versio
A volume inequality for quantum Fisher information and the uncertainty principle
Let be complex self-adjoint matrices and let be a
density matrix. The Robertson uncertainty principle gives a bound for the quantum
generalized covariance in terms of the commutators . The right side
matrix is antisymmetric and therefore the bound is trivial (equal to zero) in
the odd case .
Let be an arbitrary normalized symmetric operator monotone function and
let be the associated quantum Fisher information. In
this paper we conjecture the inequality that gives a
non-trivial bound for any natural number using the commutators . The inequality has been proved in the cases by the joint efforts
of many authors. In this paper we prove the case N=3 for real matrices
Quantum Chi-Squared and Goodness of Fit Testing
The density matrix in quantum mechanics parameterizes the statistical
properties of the system under observation, just like a classical probability
distribution does for classical systems. The expectation value of observables
cannot be measured directly, it can only be approximated by applying classical
statistical methods to the frequencies by which certain measurement outcomes
(clicks) are obtained. In this paper, we make a detailed study of the
statistical fluctuations obtained during an experiment in which a hypothesis is
tested, i.e. the hypothesis that a certain setup produces a given quantum
state. Although the classical and quantum problem are very much related to each
other, the quantum problem is much richer due to the additional optimization
over the measurement basis. Just as in the case of classical hypothesis
testing, the confidence in quantum hypothesis testing scales exponentially in
the number of copies. In this paper, we will argue 1) that the physically
relevant data of quantum experiments is only contained in the frequencies of
the measurement outcomes, and that the statistical fluctuations of the
experiment are essential, so that the correct formulation of the conclusions of
a quantum experiment should be given in terms of hypothesis tests, 2) that the
(classical) test for distinguishing two quantum states gives rise to
the quantum divergence when optimized over the measurement basis, 3)
present a max-min characterization for the optimal measurement basis for
quantum goodness of fit testing, find the quantum measurement which leads both
to the maximal Pitman and Bahadur efficiency, and determine the associated
divergence rates.Comment: 22 Pages, with a new section on parameter estimatio
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