6,301 research outputs found
The Einstein-Boltzmann Relation for Thermodynamic and Hydrodynamic Fluctuations
When making the connection between the thermodynamics of irreversible
processes and the theory of stochastic processes through the
fluctuation-dissipation theorem, it is necessary to invoke a postulate of the
Einstein-Boltzmann type. For convective processes hydrodynamic fluctuations
must be included, the velocity is a dynamical variable and although the entropy
cannot depend directly on the velocity, will depend on velocity
variations. Some authors do not include velocity variations in ,
and so have to introduce a non-thermodynamic function which replaces the
entropy and does depend on the velocity. At first sight, it seems that the
introduction of such a function requires a generalisation of the
Einstein-Boltzmann relation to be invoked. We review the reason why it is not
necessary to introduce such a function, and therefore why there is no need to
generalise the Einstein-Boltzmann relation in this way. We then obtain the
fluctuation-dissipation theorem which shows some differences as compared with
the non-convective case. We also show that is a Liapunov
function when it includes velocity fluctuations.Comment: 13 Page
Quantifying non-Gaussianity for quantum information
We address the quantification of non-Gaussianity of states and operations in
continuous-variable systems and its use in quantum information. We start by
illustrating in details the properties and the relationships of two recently
proposed measures of non-Gaussianity based on the Hilbert-Schmidt (HS) distance
and the quantum relative entropy (QRE) between the state under examination and
a reference Gaussian state. We then evaluate the non-Gaussianities of several
families of non-Gaussian quantum states and show that the two measures have the
same basic properties and also share the same qualitative behaviour on most of
the examples taken into account. However, we also show that they introduce a
different relation of order, i.e. they are not strictly monotone each other. We
exploit the non-Gaussianity measures for states in order to introduce a measure
of non-Gaussianity for quantum operations, to assess Gaussification and
de-Gaussification protocols, and to investigate in details the role played by
non-Gaussianity in entanglement distillation protocols. Besides, we exploit the
QRE-based non-Gaussianity measure to provide new insight on the extremality of
Gaussian states for some entropic quantities such as conditional entropy,
mutual information and the Holevo bound. We also deal with parameter estimation
and present a theorem connecting the QRE nonG to the quantum Fisher
information. Finally, since evaluation of the QRE nonG measure requires the
knowledge of the full density matrix, we derive some {\em experimentally
friendly} lower bounds to nonG for some class of states and by considering the
possibility to perform on the states only certain efficient or inefficient
measurements.Comment: 22 pages, 13 figures, comments welcome. v2: typos corrected and
references added. v3: minor corrections (more similar to published version
Optimal discrimination of quantum states with a fixed rate of inconclusive outcomes
In this paper we present the solution to the problem of optimally
discriminating among quantum states, i.e., identifying the states with maximum
probability of success when a certain fixed rate of inconclusive answers is
allowed. By varying the inconclusive rate, the scheme optimally interpolates
between Unambiguous and Minimum Error discrimination, the two standard
approaches to quantum state discrimination. We introduce a very general method
that enables us to obtain the solution in a wide range of cases and give a
complete characterization of the minimum discrimination error as a function of
the rate of inconclusive answers. A critical value of this rate is identified
that coincides with the minimum failure probability in the cases where
unambiguous discrimination is possible and provides a natural generalization of
it when states cannot be unambiguously discriminated. The method is illustrated
on two explicit examples: discrimination of two pure states with arbitrary
prior probabilities and discrimination of trine states
Cloning of Gaussian states by linear optics
We analyze in details a scheme for cloning of Gaussian states based on linear
optical components and homodyne detection recently demonstrated by U. L.
Andersen et al. [PRL 94 240503 (2005)]. The input-output fidelity is evaluated
for a generic (pure or mixed) Gaussian state taking into account the effect of
non-unit quantum efficiency and unbalanced mode-mixing. In addition, since in
most quantum information protocols the covariance matrix of the set of input
states is not perfectly known, we evaluate the average cloning fidelity for
classes of Gaussian states with the degree of squeezing and the number of
thermal photons being only partially known.Comment: 8 pages, 7 figure
The Seven Sisters DANCe III: Projected spatial distribution
Methods. We compute Bayesian evidences and Bayes Factors for a set of
variations of the classical radial models by King (1962), Elson et al. (1987)
and Lauer et al. (1995). The variations incorporate different degrees of model
freedom and complexity, amongst which we include biaxial (elliptical) symmetry,
and luminosity segregation. As a by-product of the model comparison, we obtain
posterior distributions and maximum a posteriori estimates for each set of
model parameters. Results. We find that the model comparison results depend on
the spatial extent of the region used for the analysis. For a circle of 11.5
parsecs around the cluster centre (the most homogeneous and complete region),
we find no compelling reason to abandon Kings model, although the Generalised
King model, introduced in this work, has slightly better fitting properties.
Furthermore, we find strong evidence against radially symmetric models when
compared to the elliptic extensions. Finally, we find that including mass
segregation in the form of luminosity segregation in the J band, is strongly
supported in all our models. Conclusions. We have put the question of the
projected spatial distribution of the Pleiades cluster on a solid probabilistic
framework, and inferred its properties using the most exhaustive and least
contaminated list of Pleiades candidate members available to date. Our results
suggest however that this sample may still lack about 20% of the expected
number of cluster members. Therefore, this study should be revised when the
completeness and homogeneity of the data can be extended beyond the 11.5
parsecs limit. Such study will allow a more precise determination of the
Pleiades spatial distribution, its tidal radius, ellipticity, number of objects
and total mass.Comment: 39 pages, 31 figure
- âŠ