Characterizing (non-)Markovianity through Fisher Information

A non-isolated physical system typically loses information to its environment, and when such loss is irreversible the evolution is said to be Markovian. Non-Markovian effects are studied by monitoring how information quantifiers, such as the distance between physical states, evolve in time. Here we show that the Fisher information metric emerges as the natural object to study in this context; we fully characterize the relation between its contractivity properties and Markovianity, both from the mathematical and operational point of view. We prove, both for classical and quantum dynamics, that Markovianity is equivalent to the monotonous contraction of the Fisher metric at all points of the set of states. At the same time, operational witnesses of non-Markovianity based on the dilation of the Fisher distance cannot, in general, detect all non-Markovian evolutions, unless specific physical postprocessing is applied to the dynamics. Finally, we show for the first time that non-Markovian dilations of Fisher distance between states at any time correspond to backflow of information about the initial state of the dynamics at time 0, via Bayesian retrodiction.Comment: comments are welcome

Quantum Fisher Information and its dynamical nature

The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich range of possible quantum Fisher information, only a handful are typically used and studied. This review aims at collecting a number of results scattered in the literature that can be useful to people who begin the study of Fisher information and to those who are already working on it to have a more organic understanding of the topic. Moreover, we complement the review with new results about the relation between Fisher information and physical evolutions. Extending the study done in [1], we prove that all the physically realisable dynamics can be defined solely in terms of their relation with respect to the Fisher information metric. Moreover, other properties as Markovianity, retrodiction or detailed balance can be expressed in the same formalism. These results show a fact that was partially overseen in the literature, namely the inherently dynamical nature of Fisher information.Comment: 36 pages of main text, 15 of additional information, 12 of appendix, and one of inde

Physicality of evolution and statistical contractivity are equivalent notions of maps

Statistical quantifiers are generically required to contract under physical evolutions, following the intuition that information should be lost under noisy transformations. This principle is very relevant in statistics, and it even allows to derive uniqueness results based on it: by imposing their contractivity under any physical maps, the Chentsov-Petz theorem singles out a unique family of metrics on the space of probability distributions (or density matrices) called the Fisher information metrics. This result might suggest that statistical quantifiers are a derived concept, as their very definition is based on physical maps. The aim of this work is to disprove this belief. Indeed, we present a result dual to the Chentsov-Petz theorem, proving that among all possible linear maps, the only ones that contract the Fisher information are exactly the physical ones. This result shows that, contrary to the common opinion, there is no fundamental hierarchy between physical maps and canonical statistical quantifiers, as either of them can be defined in terms of the other

Design of Self-Healing Key Distribution Schemes

A self-healing key distribution scheme enables dynamic groups of users of an unreliable network to establish group keys for secure communication. In such a scheme, a group manager, at the beginning of each session, in order to provide a key to each member of the group, sends packets over a broadcast channel. Every user, belonging to the group, computes the group key by using the packets and some private information. The group manager can start multiple sessions during a certain time-interval, by adding/removing users to/from the initial group. The main property of the scheme is that, if during a certain session some broadcasted packet gets lost, then users are still capable of recovering the group key for that session simply by using the packets they have received during a previous session and the packets they will receive at the beginning of a subsequent one, without requesting additional transmission from the group manager. Indeed, the only requirement that must be satisfied, in order for the user to recover the lost keys, is membership in the group both before and after the sessions in which the broadcast messages containing the keys are sent. This novel and appealing approach to key distribution is quite suitable in certain military applications and in several Internet-related settings, where high security requirements need to be satisfied. In this paper we continue the study of self-healing key distribution schemes, introduced by Staddon et al. [37]. We analyze some existing constructions: we show an attack that can be applied to one of these constructions, in order to recover session keys, and two problems in another construction. Then, we present a new mechanism for implementing the self-healing approach, and we present an efficient construction which is optimal in terms of user memory storage. Finally, we extend the self-healing approach to key distribution, and we present a scheme which enables a user to recover from a single broadcast message all keys associated with sessions in which he is member of the communication group

HISTORY, MEMORY AND GEOGRAPHY - AN HISTORICAL GIS ON THE OPERATION OF THE ITALIAN ARMY DURING THE RUSSIAN CAMPAIGN (1941-1943)

Attraverso l’analisi di documentazione testuale e cartografica, è stata realizzata una ricostruzione dinamica degli eventi legati alla partecipazione dell’Italia all’invasione nazista della Russia. Il progetto è stato realizzato utilizzando la tecnologia GIS, che ha consentito di integrare dati storici e geografici fornendo una modalità innovativa per la visualizzazione e l’interrogazione dei dati. È stato possibile stratificare i dati raccolti in una serie di livelli informativi, ricreando e rileggendo gli eventi storici. Una volta completato lo sviluppo del GIS è stato realizzato un webGIS per la consultazione online dei risultati del progetto.Through the analysis of documents and cartography, a dynamic reconstruction of historical events occurred during the participation of the Italian Army to the Nazi’s invasion of Russia was performed. The goal was reached using Geographic Information Systems (GIS) that allow to integrate geographic and historical data providing a new way for the visualization and querying of locations and shapes related to data. Through GIS, it is possible to “stratify” data collected in information levels and recreate and “re-read” historical events. After the development of the GIS, an online GIS was developed as an interface for consulting information via web

Noi mi...? A volte sì!

La consulenza affronta il tema della reggenza verbale di verbi che presentano come primo argomento (soggetto) il pronome di prima persona plurale e come secondo argomento (oggetto, diretto o indiretto) il pronome di prima persona singolare espresso da un clitico

On Unconditionally Secure Distributed Oblivious Transfer.

This paper is about the Oblivious Transfer in the distributed model proposed by M. Naor and B. Pinkas. In this setting a Sender has n secrets and a Receiver is interested in one of them. During a set up phase, the Sender gives information about the secrets to m Servers. Afterwards, in a recovering phase, the Receiver can compute the secret she wishes by interacting with any k of them. More precisely, from the answers received she computes the secret in which she is interested but she gets no information on the others and, at the same time, any coalition of k − 1 Servers can neither compute any secret nor figure out which one the Receiver has recovered. We present an analysis and new results holding for this model: lower bounds on the resources required to implement such a scheme (i.e., randomness, memory storage, communication complexity); some impossibility results for one-round distributed oblivi- ous transfer protocols; two polynomial-based constructions implementing 1-out-of-n dis- tributed oblivious transfer, which generalize and strengthen the two constructions for 1-out-of-2 given by Naor and Pinkas; as well as new one-round and two-round distributed oblivious transfer protocols, both for threshold and general access structures on the set of Servers, which are optimal with respect to some of the given bounds. Most of these constructions are basically combinatorial in nature

The use of x-ray CT and MRI in the study of sacroiliac joints in patients with Behcet disease and acute anterior uveitis

Objective: It's controversial if Behcet Disease (BD) must be included in the group of seronegative spondyloarthropathy (SpA). Our aim was to establish the prevalence of sacroiliitis (SI) in patients with BD using X-Ray, CT and MRI, in comparison with patients with Acute Anterior Uveitis (AAU), that is known to belong to the subgroups of SpA. Methods: We considered, in the period from 04/2006 to 04/2009, 21 consecutive patients with BD, positive for HLA B51 and 28 consecutive patients with AAU, positive for HLA B27. These patients were previously selected by our Rheumatological Ward. Altogether we evaluated 98 sacroiliac joints (SIJ); each side of any patient was graded separately. Results: X-ray of the pelvis showed advanced SI (grade 4) in 14% of the cases in patients with AAU; in BD group only 7% CT showed advanced SI in 14% within AAU patients versus 6-12% of advanced SI (right to left) within BD patients. MR showed 14% of advanced SI (bilateral) within AAU versus 6-11% of advanced SI (right to left) in BD patients. Conclusions: This study supports the trend to not consider BD within the SpA, being the prevalence of SI in BD patients not very different from general population and anyway lower than that observed in patients with AAU. On the other side the prevalence of SI in AAU patients is higher than in BD patients and very similar to the one observed in patients with seronegative arthritis, and anyway high enough to consider joint involvement as an important feature of the disease

Search for Electron Capture in 176^{176}Lu with LYSO scintillator

The nuclide $^{176}$Lu is one of the few naturally occurring isotopes that are potentially unstable with respect to electron capture (EC). Although experimental evidence for $^{176}$Lu EC decay is still missing, this isotope is instead well known to $\beta^-$ decay into $^{176}$Hf with an half-life of about 38 Gyr. The precise investigation of all $^{176}$Lu possible decay modes is interesting because the Lu/Hf ratio is adopted as an isotopic clock. Previous searches for the $^{176}$Lu EC decay were performed by using a passive Lutetium source coupled with an HP-Ge spectrometer. Our approach uses a LYSO crystal both as Lutetium source and as an active detector. Scintillation light from the LYSO crystal is acquired in coincidence with the signals from the HP-Ge detector, this allows a powerful suppression of the background sourcing from the well known $\beta^-$ decay branch. This coincidence approach led to an improvement on the $^{176}$Lu EC branching ratio limits by a factor 3 to 30, depending on the considered EC channel.Comment: 8 pages, 12 figure