Metric on the space of quantum states from relative entropy. Tomographic reconstruction

In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential calculus. The cases N = 2, N = 3 are discussed in detail and notable limits are analyzed. The radial limit procedure has been used to recover quantum metrics for lower rank states, such as pure states. By using the tomographic picture of quantum mechanics we have obtained the Fisher- Rao metric for the space of quantum tomograms and derived a reconstruction formula of the quantum metric of density states out of the tomographic one. A new inequality obtained for probabilities of three spin-1/2 projections in three perpendicular directions is proposed to be checked in experiments with superconducting circuits.Comment: 31 pages. No figures. Abstract and Introduction rewritten. Minor corrections. References adde

Formazione specifica e continua in medicina generale: le scelte della SIMG

Aim of this paper is to describe two educational programs involving primary care physicians that are very changed in recent years in our country. The first is the preparatory training that medical graduates must attend before start to practice as family physicians in the NHS; in Italy this training is mandatory since  the early ’90s. The second are the educational activities carried out within the mandatory Italian system of Continuing Medical Education. For both programs, the Author explains the methodological choices proposed and implemented by SIMG (Italian Society of General Medicine and Primary Care)

Stratified Manifold of Quantum States, actions of the complex special linear group

We review the geometry of the space of quantum states $\mathscr{S}(\mathcal{H})$ of a finite-level quantum system with Hilbert space $\mathcal{H}$ from a group-theoretical point of view. This space carries two stratifications generated by the action of two different Lie groups: the special unitary group $\mathcal{SU}(\mathcal{H})$ and its complexification $\mathcal{SL}(\mathcal{H})$, the complex special linear group. A stratum of the stratification generated by $\mathcal{SU}(\mathcal{H})$ is composed of isospectral states, that is, density operators with the same spectrum, A stratum of the stratification generated by $\mathcal{SL}(\mathcal{H})$ is composed of quantum states with the same rank. We prove that on every submanifold of isospectral quantum states there is also a canonical left action of $\mathcal{SL}(\mathcal{H})$ which is related with the canonical K\"{a}hler structure on isospectral quantum states. The fundamental vector fields of this $\mathcal{SL}(\mathcal{H})$-action are divided into Hamiltonian and gradient vector fields. The former give rise to invertible maps on $\mathscr{S}(\mathcal{H})$ that preserve the von Neumann entropy and the convex structure of $\mathscr{S}(\mathcal{H})$, while the latter give rise to invertible maps on $\mathscr{S}(\mathcal{H})$ that preserve the von Neumann entropy but not the convex structure of $\mathscr{S}(\mathcal{H})$. A similar decomposition is given for the $\mathcal{SL}(\mathcal{H})$-action generating the stratification of $\mathscr{S}(\mathcal{H})$ into manifolds of quantum states with the same rank, where gradient vector fields preserve the rank but do not preserve entropy. Some comments on multipartite quantum systems are made. It is proved that the sets of product states of a multipartite quantum system are homogeneous manifolds for the action of the complex special linear group associated with the partition

A Pedagogical Intrinsic Approach to Relative Entropies as Potential Functions of Quantum Metrics: the qq-zz Family

The so-called $q$-z-\textit{R\'enyi Relative Entropies} provide a huge two-parameter family of relative entropies which includes almost all well-known examples of quantum relative entropies for suitable values of the parameters. In this paper we consider a log-regularized version of this family and use it as a family of potential functions to generate covariant $(0,2)$ symmetric tensors on the space of invertible quantum states in finite dimensions. The geometric formalism developed here allows us to obtain the explicit expressions of such tensor fields in terms of a basis of globally defined differential forms on a suitable unfolding space without the need to introduce a specific set of coordinates. To make the reader acquainted with the intrinsic formalism introduced, we first perform the computation for the qubit case, and then, we extend the computation of the metric-like tensors to a generic $n$-level system. By suitably varying the parameters $q$ and $z$, we are able to recover well-known examples of quantum metric tensors that, in our treatment, appear written in terms of globally defined geometrical objects that do not depend on the coordinates system used. In particular, we obtain a coordinate-free expression for the von Neumann-Umegaki metric, for the Bures metric and for the Wigner-Yanase metric in the arbitrary $n$-level case.Comment: 50 pages, 1 figur

Condivisione anziché delibere: dalla formazione sul campo alla valutazione del cambiamento

È stato progettato e condotto nel 2012 un intervento formativo in presenza e sul campo, indirizzato all’appropriatezza prescrittiva di PSA, VES, PCR e degli esami prima di terapia estro-progestinica. Tutti i 430 medici di medicina generale (MMG) della ASL TO3, suddivisi in 28 equipe locali di circa 20 medici l’una, hanno partecipato a 2 incontri in plenaria, intercalati da lavoro personale e di equipe sui propri comportamenti prescrittivi. Il Controllo di Gestione della ASL ha evidenziato una diminuzione complessiva del 29% della prescrizione degli esami in oggetto, con un range per i singoli esami fra 10 e 56%, nonché una diminuzione complessiva del 15,59% di tutte le richieste di esami di laboratorio.Introduction. Following an act of Piemonte region about the appropriateness of lab test orders, a project of blended education (front and “learning on the job” education) was designed and implemented, with the aim of increasing the knowledge and awareness of General Practitioners (GP) about the appropriateness of orders of a set of lab tests (PSA, VES, PCR, tests for risk assessment before estro-progestinic medication). The main expected outcome was a change in order habits, with a decrease in the number of inappropriate orders. A “halo effect” was expected as well, showed by a decrease in orders of other lab tests than the ones addressed by the educational program. Methods. The project was designed according to the nine phases of PRECEDE-PROCEED model, particularly addressed to identify effective assessment models for interventions of improvement of health and to assist their implementation and evaluation. All 430 GPs of the local Health Trust ASL TO3 were involved and joined the project, organized in 28 local teams of about 20 members each. The educational program was held in 2012 and was based on two class general meetings (introduction of the project, guidelines for the appropriateness of orders, interim report on the activities of local teams, final report on results and suggestions), intertwined with local team meetings, in which the members of the teams reported about the audit of their behavior and about the mechanisms they identified as a cause of inappropriate ordering. Many of the teams displayed the characteristics of community of practice, with a reflective and active attitude. Results. At the end of the project the orders addressed by the educational program decreased overall of 29%, with the decrease of single exams ranging from 10 to 56%. This decrease corresponded to a decrease of € 523,471 of cost. Many feedback emerged from the local teams, pointing to the influence that the dispositions from consultants had in the process of request of lab tests. As a by-product, data from the ASL TO3 management control office showed a decrease of 15.59% of all lab tests in 2012

Anthropometric characteristics of young Italian tennis players

Purpose. Aim of our study is to observe specific body differences induced by training in young agonist tennis players at pre-pubertal and pubertal age, using anthropometry. Method. We analyzed 101 tennis players (27 females and 74 males) coming from South Italy, aged 8-14, which played tennis from at least 1 year. Anthropometric measurements like wrist, mid-thigh, mid-arm circumferences and arms length were compared between dominant and not dominant side of the body. Results. The mean Z-score for females was 0.9627, corresponding to the 83.22th centile of Italian growth chart, the mean Z-score for males was 1.0157, corresponding to 84.51th centile of Italian growth chart. For weight the mean Z-score for females was 0.2394 (59.46th centile) and the mean Z-score for males was 0.4032 (65.66th centile). The mean Z-score for females Body Mass Index was -0.1451 (44.23th centile), instead the mean Z-score for males was -0.0768 (46.94th centile). The Wilcoxon test reported a statistically significant difference between dominant and not dominant wrist circumferences regardless of sex (p-value=1.87e-10). Conclusions. Our study revealed that playing tennis starting from childhood may be useful for a regular growth. Analysis of wrist circumference and height may confirm the osteogenic potential of the sport

Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.Comment: 8 page