9,089 research outputs found
On positive maps, entanglement and quantization
We outline the scheme for quantization of classical Banach space results
associated with some prototypes of dynamical maps and describe the quantization
of correlations as well. A relation between these two areas is discussed
On Kolgomorov-Sinai entropy and its quantization
In the paper we present the new approach to Kolmogorov-Sinai entropy and its
quantization. Our presentation stems from an application of the Choquet theory
to the theory of decompositions of states and therefore, it resembles our
rigorous description of entanglement of formationComment: 10 page
Some remarks on separability of states
Several problems concerning separable states are clarified on the basis of
Choi's scheme and old Kadison and Tomiyama results. Moreover, we generalize
Terhal's construction of positive maps.Comment: 12 page
Quantum correlations; quantum probability approach
This survey gives a comprehensive account of quantum correlations understood
as a phenomenon stemming from the rules of quantization. Centered on quantum
probability it describes the physical concepts related to correlations (both
classical and quantum), mathematical structures, and their consequences. These
include the canonical form of classical correlation functionals, general
definitions of separable (entangled) states, definition and analysis of
quantumness of correlations, description of entanglement of formation, and PPT
states. This work is intended both for physicists interested not only in
collection of results but also in the mathematical methods justifying them, and
mathematicians looking for an application of quantum probability to concrete
new problems of quantum theory.Comment: Revised version, Minor improvements. Typos fixe
On the origin of non-decomposable maps
The Radon-Nikodym formalism is used to study the structure of the set of
positive maps from into itself, where
is a finite dimensional Hilbert space. In particular, this formalism was
employed to formulate simple criteria which ensure that certain maps are non
decomposable. In that way, a recipe for construction of non decomposable maps
was obtained.Comment: Incorrect example given in subsection 5.5 was remove
On positive maps in quantum information
Using Grothendieck approach to the tensor product of locally convex spaces we
review a characterization of positive maps as well as Belavkin-Ohya
characterization of PPT states. Moreover, within this scheme, \textit{ a
generalization of the idea of Choi matrices for genuine quantum systems will be
presented}.Comment: Paper dedicated to the memory of Viacheslav "Slava" Belavkin. arXiv
admin note: text overlap with arXiv:1005.394
Does quantum chaos exist? (A quantum Lyapunov exponents approach.)
We shortly review the progress in the domain of deterministic chaos for
quantum dynamical systems. With the appropriately extended definition of
quantum Lyapunov exponent we analyze various quantum dynamical maps. It is
argued that, within Quantum Mechanics, irregular evolution for properly chosen
observables can coexist with regular and predictable evolution of states.Comment: Latex, 28 page
A note on Stormer condition for decomposability of positive maps
We present a partial characterization of matrices in M_n(\cA)^+ satisfying
the St{\o}rmer condition.Comment: 5 page
On a characterization of PPT states
We present two different descriptions of positive partially transposed (PPT)
states. One is based on the theory of positive maps while the second
description provides a characterization of PPT states in terms of Hilbert space
vectors. Our note is based on our previous results.Comment: a report based on previous result
Analyticity and Quark-Gluon Structure of Hadrons
The amplitudes of hadron-hadron forward elastic scattering at high energy a
re investigated on the basis of analiticity and crossing-symmetry which is
valid in QCD. The universal uniformizing variable for them is proposed and the
formulae for crossing-even and crossing-odd amplitudes are derived. The same
parameters in these formulae determine the real and imaginary (total cross
sections) parts of the amplitudes. The analysis of the parameters determined
from experimental data clearly points to the quark-gluon stracture of hadrons.
The total cross sections for hyperon-proton scattering are predicted. They are
consistent with experimental data and, in particular, with the new
SELEX-collaboration measurement .Comment: 7 pages, LaTe
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