2,003 research outputs found
Properties of Classical and Quantum Jensen-Shannon Divergence
Jensen-Shannon divergence (JD) is a symmetrized and smoothed version of the
most important divergence measure of information theory, Kullback divergence.
As opposed to Kullback divergence it determines in a very direct way a metric;
indeed, it is the square of a metric. We consider a family of divergence
measures (JD_alpha for alpha>0), the Jensen divergences of order alpha, which
generalize JD as JD_1=JD. Using a result of Schoenberg, we prove that JD_alpha
is the square of a metric for alpha lies in the interval (0,2], and that the
resulting metric space of probability distributions can be isometrically
embedded in a real Hilbert space. Quantum Jensen-Shannon divergence (QJD) is a
symmetrized and smoothed version of quantum relative entropy and can be
extended to a family of quantum Jensen divergences of order alpha (QJD_alpha).
We strengthen results by Lamberti et al. by proving that for qubits and pure
states, QJD_alpha^1/2 is a metric space which can be isometrically embedded in
a real Hilbert space when alpha lies in the interval (0,2]. In analogy with
Burbea and Rao's generalization of JD, we also define general QJD by
associating a Jensen-type quantity to any weighted family of states.
Appropriate interpretations of quantities introduced are discussed and bounds
are derived in terms of the total variation and trace distance.Comment: 13 pages, LaTeX, expanded contents, added references and corrected
typo
On the valence bond solid in the presence of Dzyaloshinskii-Moriya interaction
We examine the stability of the valence bond solid (VBS) phase against the
Dzyaloshinskii-Moriya (DM) interaction in the bipartite lattice. Despite the
VBS is vulnerable against the antiferromagnetic interaction, for example in the
Q-J model proposed by Sandvik, where the quantum phase transition occurs at
, we found that on the contrary the VBS is very stable against
the DM interaction. The quantum phase transition does not occur until D/Q goes
to infinity, where D is the strength of the DM interaction. The VBS in the ALKT
model and the Haldane gap system also exhibit the same property.Comment: 5 pages and 5 figure
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Tools for efficient analysis of concurrent software systems
The ever increasing use of distributed computing as a method of providing added computing power and reliability has sparked interest in methods to model and analyze concurrent hardware/ software systems. Efficient automated analysis tools are needed to aid designers of such systems. The Distributed Systems Project at UCI has been developing a suite of tools (dubbed the P-NUT system) which supports efficient analysis of models of concurrent software. This paper presents the principles which guide the development of P-NUT tools and discusses the development of one of the tools: the Reachability Graph Builder (RGB). The P-NUT approach to tool development has resulted in the production of a highly efficient tool for constructing reachability graphs. The careful design of data structures and associated algorithms has significantly enlarged the class of models which can be analyzed
Theoretical description of deformed proton emitters: nonadiabatic coupled-channel method
The newly developed nonadiabatic method based on the coupled-channel
Schroedinger equation with Gamow states is used to study the phenomenon of
proton radioactivity. The new method, adopting the weak coupling regime of the
particle-plus-rotor model, allows for the inclusion of excitations in the
daughter nucleus. This can lead to rather different predictions for lifetimes
and branching ratios as compared to the standard adiabatic approximation
corresponding to the strong coupling scheme. Calculations are performed for
several experimentally seen, non-spherical nuclei beyond the proton dripline.
By comparing theory and experiment, we are able to characterize the angular
momentum content of the observed narrow resonance.Comment: 12 pages including 10 figure
On amplitudes in self-dual sector of Yang-Mills theory
Self-dual perturbiner in the Yang-Mills theory is constructed by the twistor
methods both in topologically trivial and topologically nontrivial cases.
Maximally helicity violating amplitudes and their instanton induced analogies
are briefly discussed.Comment: 9 pages, Latex, a misguided reference is corrected, ps is also
available at http://wwwtheor.itep.ru/preprints/1996
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