445 research outputs found
Continuity bounds on the quantum relative entropy
The quantum relative entropy is frequently used as a distance, or
distinguishability measure between two quantum states. In this paper we study
the relation between this measure and a number of other measures used for that
purpose, including the trace norm distance. More precisely, we derive lower and
upper bounds on the relative entropy in terms of various distance measures for
the difference of the states based on unitarily invariant norms. The upper
bounds can be considered as statements of continuity of the relative entropy
distance in the sense of Fannes. We employ methods from optimisation theory to
obtain bounds that are as sharp as possible.Comment: 13 pages (ReVTeX), 3 figures, replaced with published versio
Parameter estimation in pair hidden Markov models
This paper deals with parameter estimation in pair hidden Markov models
(pair-HMMs). We first provide a rigorous formalism for these models and discuss
possible definitions of likelihoods. The model being biologically motivated,
some restrictions with respect to the full parameter space naturally occur.
Existence of two different Information divergence rates is established and
divergence property (namely positivity at values different from the true one)
is shown under additional assumptions. This yields consistency for the
parameter in parametrization schemes for which the divergence property holds.
Simulations illustrate different cases which are not covered by our results.Comment: corrected typo
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
Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics
A consistent generalization of statistical mechanics is obtained by applying
the maximum entropy principle to a trace-form entropy and by requiring that
physically motivated mathematical properties are preserved. The emerging
differential-functional equation yields a two-parameter class of generalized
logarithms, from which entropies and power-law distributions follow: these
distributions could be relevant in many anomalous systems. Within the specified
range of parameters, these entropies possess positivity, continuity, symmetry,
expansibility, decisivity, maximality, concavity, and are Lesche stable. The
Boltzmann-Shannon entropy and some one parameter generalized entropies already
known belong to this class. These entropies and their distribution functions
are compared, and the corresponding deformed algebras are discussed.Comment: Version to appear in PRE: about 20% shorter, references updated, 13
PRE pages, 3 figure
Security of Quantum Key Distribution with entangled quNits
We consider a generalisation of Ekert's entanglement-based quantum
cryptographic protocol where qubits are replaced by quits (i.e.,
N-dimensional systems). In order to study its robustness against optimal
incoherent attacks, we derive the information gained by a potential
eavesdropper during a cloning-based individual attack. In doing so, we
generalize Cerf's formalism for cloning machines and establish the form of the
most general cloning machine that respects all the symmetries of the problem.
We obtain an upper bound on the error rate that guarantees the confidentiality
of quNit generalisations of the Ekert's protocol for qubits.Comment: 15 pages, equation 15 and conclusions corrected the 14th of April
2003, new results adde
Complexity Measures from Interaction Structures
We evaluate new complexity measures on the symbolic dynamics of coupled tent
maps and cellular automata. These measures quantify complexity in terms of
-th order statistical dependencies that cannot be reduced to interactions
between units. We demonstrate that these measures are able to identify
complex dynamical regimes.Comment: 11 pages, figures improved, minor changes to the tex
A Bivariate Measure of Redundant Information
We define a measure of redundant information based on projections in the
space of probability distributions. Redundant information between random
variables is information that is shared between those variables. But in
contrast to mutual information, redundant information denotes information that
is shared about the outcome of a third variable. Formalizing this concept, and
being able to measure it, is required for the non-negative decomposition of
mutual information into redundant and synergistic information. Previous
attempts to formalize redundant or synergistic information struggle to capture
some desired properties. We introduce a new formalism for redundant information
and prove that it satisfies all the properties necessary outlined in earlier
work, as well as an additional criterion that we propose to be necessary to
capture redundancy. We also demonstrate the behaviour of this new measure for
several examples, compare it to previous measures and apply it to the
decomposition of transfer entropy.Comment: 16 pages, 15 figures, 1 table, added citation to Griffith et al 2012,
Maurer et al 199
Controlling orbital moment and spin orientation in CoO layers by strain
We have observed that CoO films grown on different substrates show dramatic
differences in their magnetic properties. Using polarization dependent x-ray
absorption spectroscopy at the Co L edges, we revealed that the
magnitude and orientation of the magnetic moments strongly depend on the strain
in the films induced by the substrate. We presented a quantitative model to
explain how strain together with the spin-orbit interaction determine the 3d
orbital occupation, the magnetic anisotropy, as well as the spin and orbital
contributions to the magnetic moments. Control over the sign and direction of
the strain may therefore open new opportunities for applications in the field
of exchange bias in multilayered magnetic films
Universal Quantum Information Compression
Suppose that a quantum source is known to have von Neumann entropy less than
or equal to S but is otherwise completely unspecified. We describe a method of
universal quantum data compression which will faithfully compress the quantum
information of any such source to S qubits per signal (in the limit of large
block lengths).Comment: RevTex 4 page
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