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 $10^o-15^o$ the value of $\gamma$ extracted via the overall fit to the $B \to PP$ 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 $h$. 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 $h=0$ we reproduce the rigorously known asymptotic temperature dependence of the free energy. For $h \ne 0$, 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 B→VVB \to VV Transitions

Measurements of polarization fractions in $B \to VV$ transitions, with $V$ a light vector meson, show that the longitudinal amplitude dominates in $B^0 \to \rho^+ \rho^-$, $B^+ \to \rho^+ \rho^0$, and $B^+ \to \rho^0 K^{*+}$ decays and not in the penguin induced decays $B^0 \to \phi K^{*0}$, $B^+ \to \phi K^{*+}$. We study the effect of rescattering mediated by charmed resonances, finding that in $B \to \phi K^*$ it can be responsible of the suppression of the longitudinal amplitude. For the decay $B \to \rho K^*$ we find that the longitudinal fraction cannot be too large without invoking new effects.Comment: LaTex, 14 pages, 3 figure