1,057 research outputs found
Wigner-Yanase information on quantum state space:the geometric approach
In the search of appropriate riemannian metrics on quantum state space the
concept of statistical monotonicity, or contraction under coarse graining, has
been proposed by Chentsov. The metrics with this property have been classified
by Petz. All the elements of this family of geometries can be seen as quantum
analogues of Fisher information. Although there exists a number of general
theorems sheding light on this subject, many natural questions, also stemming
from applications, are still open. In this paper we discuss a particular member
of the family, the Wigner-Yanase information.
Using a well-known approach that mimics the classical pull-back approach to
Fisher information, we are able to give explicit formulae for the geodesic
distance, the geodesic path, the sectional and scalar curvatures associated to
Wigner-Yanase information. Moreover we show that this is the only monotone
metric for which such an approach is possible
A characterisation of Wigner-Yanase skew information among statistically monotone metrics
Let M-n = M-n(C) be the space of n x n complex matrices endowed with the Hilbert-Schmidt scalar product, let S-n be the unit sphere of M-n and let D-n subset of M-n be the space of strictly positive density matrices. We show that the scalar product over D-n introduced by Gibilisco and Isola(3) (that is the scalar product induced by the map D-n There Exists rho --> rootrho is an element of S-n) coincides with the Wigner-Yanase monotone metric
Fisher information and Stam inequality on a finite group
We prove a discrete version of the Stam inequality for random variables taking values on a finite group
A dynamical uncertainty principle in von Neumann algebras by operator monotone functions
Suppose that A(1),..., A(N) are observables (selfadjoint matrices) and rho is a state (density matrix). In this case the standard uncertainty principle, proved by Robertson, gives a bound for the quantum generalized variance, namely for det{Cov(rho) (A(j), A(k) )}, using the commutators [A(j), A(k)]; this bound is trivial when N is odd. Recently a different inequality of Robertson-type has been proved by the authors with the help of the theory of operator monotone functions. In this case the bound makes use of the commutators [rho, A(j)] and is non-trivial for any N. In the present paper we generalize this new result to the von Neumann algebra case. Nevertheless the proof appears to simplify all the existing ones
On the monotonicity of scalar curvature in classical and quantum information geometry
We study the statistical monotonicity of the scalar curvature for the
alpha-geometries on the simplex of probability vectors. From the results
obtained and from numerical data we are led to some conjectures about quantum
alpha-geometries and Wigner-Yanase-Dyson information. Finally we show that this
last conjecture implies the truth of the Petz conjecture about the monotonicity
of the scalar curvature of the Bogoliubov-Kubo-Mori monotone metric.Comment: 20 pages, 2 .eps figures; (v2) section 2 rewritten, typos correcte
Charming penguins in B -> PP decays and the extraction of gamma
It is shown that inclusion of charming penguins of the size suggested by
short-distance dynamics may shift down by the value of
extracted via the overall fit to the branching ratios. A
substantial dependence of the fit on their precise values is found,
underscoring the need to improve the reliability of data.Comment: 11 pages, 1 figure, v2 - references reordere
Cluster Approximation for the Farey Fraction Spin Chain
We consider the Farey fraction spin chain in an external field . Utilising
ideas from dynamical systems, the free energy of the model is derived by means
of an effective cluster energy approximation. This approximation is valid for
divergent cluster sizes, and hence appropriate for the discussion of the
magnetizing transition. We calculate the phase boundaries and the scaling of
the free energy. At we reproduce the rigorously known asymptotic
temperature dependence of the free energy. For , our results are
largely consistent with those found previously using mean field theory and
renormalization group arguments.Comment: 17 pages, 3 figure
The Riddle of Polarization in Transitions
Measurements of polarization fractions in transitions, with a
light vector meson, show that the longitudinal amplitude dominates in , , and decays and
not in the penguin induced decays , .
We study the effect of rescattering mediated by charmed resonances, finding
that in it can be responsible of the suppression of the
longitudinal amplitude. For the decay we find that the
longitudinal fraction cannot be too large without invoking new effects.Comment: LaTex, 14 pages, 3 figure
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