972 research outputs found
Fluctuations of the partial filling factors in competitive RSA from binary mixtures
Competitive random sequential adsorption on a line from a binary mix of
incident particles is studied using both an analytic recursive approach and
Monte Carlo simulations. We find a strong correlation between the small and the
large particle distributions so that while both partial contributions to the
fill factor fluctuate widely, the variance of the total fill factor remains
relatively small. The variances of partial contributions themselves are quite
different between the smaller and the larger particles, with the larger
particle distribution being more correlated. The disparity in fluctuations of
partial fill factors increases with the particle size ratio. The additional
variance in the partial contribution of smaller particle originates from the
fluctuations in the size of gaps between larger particles. We discuss the
implications of our results to semiconductor high-energy gamma detectors where
the detector energy resolution is controlled by correlations in the cascade
energy branching process.Comment: 19 pages, 8 figure
A Classical Bound on Quantum Entropy
A classical upper bound for quantum entropy is identified and illustrated,
, involving the variance
in phase space of the classical limit distribution of a given system. A
fortiori, this further bounds the corresponding information-theoretical
generalizations of the quantum entropy proposed by Renyi.Comment: Latex2e, 7 pages, publication versio
A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations
We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC)
for the purpose of calculating the Renyi entanglement entropies and associated
mutual information. The algorithm converges an estimate for an analogue to the
density of states for Stochastic Series Expansion QMC allowing a direct
calculation of Renyi entropies without explicit thermodynamic integration. We
benchmark results for the mutual information on two-dimensional (2D) isotropic
and anisotropic Heisenberg models, 2D transverse field Ising model, and 3D
Heisenberg model, confirming a critical scaling of the mutual information in
cases with a finite-temperature transition. We discuss the benefits and
limitations of broad sampling techniques compared to standard importance
sampling methods.Comment: 9 pages, 7 figure
Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles
5 pages, 1 figur
Information theoretical properties of Tsallis entropies
A chain rule and a subadditivity for the entropy of type , which is
one of the nonadditive entropies, were derived by Z.Dar\'oczy. In this paper,
we study the further relations among Tsallis type entropies which are typical
nonadditive entropies. The chain rule is generalized by showing it for Tsallis
relative entropy and the nonadditive entropy. We show some inequalities related
to Tsallis entropies, especially the strong subadditivity for Tsallis type
entropies and the subadditivity for the nonadditive entropies. The
subadditivity and the strong subadditivity naturally lead to define Tsallis
mutual entropy and Tsallis conditional mutual entropy, respectively, and then
we show again chain rules for Tsallis mutual entropies. We give properties of
entropic distances in terms of Tsallis entropies. Finally we show
parametrically extended results based on information theory.Comment: The subsection on data processing inequality was deleted. Some typo's
were modifie
Collapse of the quantum correlation hierarchy links entropic uncertainty to entanglement creation
Quantum correlations have fundamental and technological interest, and hence
many measures have been introduced to quantify them. Some hierarchical
orderings of these measures have been established, e.g., discord is bigger than
entanglement, and we present a class of bipartite states, called premeasurement
states, for which several of these hierarchies collapse to a single value.
Because premeasurement states are the kind of states produced when a system
interacts with a measurement device, the hierarchy collapse implies that the
uncertainty of an observable is quantitatively connected to the quantum
correlations (entanglement, discord, etc.) produced when that observable is
measured. This fascinating connection between uncertainty and quantum
correlations leads to a reinterpretation of entropic formulations of the
uncertainty principle, so-called entropic uncertainty relations, including ones
that allow for quantum memory. These relations can be thought of as
lower-bounds on the entanglement created when incompatible observables are
measured. Hence, we find that entanglement creation exhibits complementarity, a
concept that should encourage exploration into "entanglement complementarity
relations".Comment: 19 pages, 2 figures. Added Figure 1 and various remarks to improve
clarity of presentatio
Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
We present a general scheme for the calculation of the Renyi entropy of a
subsystem in quantum many-body models that can be efficiently simulated via
quantum Monte Carlo. When the simulation is performed at very low temperature,
the above approach delivers the entanglement Renyi entropy of the subsystem,
and it allows to explore the crossover to the thermal Renyi entropy as the
temperature is increased. We implement this scheme explicitly within the
Stochastic Series expansion as well as within path-integral Monte Carlo, and
apply it to quantum spin and quantum rotor models. In the case of quantum
spins, we show that relevant models in two dimensions with reduced symmetry (XX
model or hardcore bosons, transverse-field Ising model at the quantum critical
point) exhibit an area law for the scaling of the entanglement entropy.Comment: 5+1 pages, 4+1 figure
Random databases with correlated data
A model of random databases is given, with arbitrary correlations among the data of one individual. This is given by a joint distribution function. The individuals are chosen independently, their number m is considered to be (approximately) known. The probability of the event that a given functional dependency A → b holds (A is a set of attributes, b is an attribute) is determined in a limiting sense. This probability is small if m is much larger than and is large if m is much smaller than 2 H 2(A→b)/ 2 where H 2(A→b) is an entropy like functional of the probability distribution of the data. © 2012 Springer-Verlag Berlin Heidelberg
In a search for a shape maximizing packing fraction for two-dimensional random sequential adsorption
Random sequential adsorption (RSA) of various two dimensional objects is
studied in order to find a shape which maximizes the saturated packing
fraction. This investigation was begun in our previous paper [Cie\'sla et al.,
Phys. Chem. Chem. Phys. 17, 24376 (2015)], where the densest packing was
studied for smoothed dimers. Here this shape is compared with a smoothed
-mers, spherocylinders and ellipses. It is found that the highest packing
fraction out of the studied shapes is and is obtained for
ellipses having long-to-short axis ratio of , which is also the largest
anisotropy among the investigated shapes.Comment: 14 pages, 7 fiure
Collision entropy and optimal uncertainty
We propose an alternative measure of quantum uncertainty for pairs of
arbitrary observables in the 2-dimensional case, in terms of collision
entropies. We derive the optimal lower bound for this entropic uncertainty
relation, which results in an analytic function of the overlap of the
corresponding eigenbases. Besides, we obtain the minimum uncertainty states. We
compare our relation with other formulations of the uncertainty principle.Comment: The manuscript has been accepted for publication as a Regular Article
in Physical Review
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