Chirality from quantum walks without quantum coin

Quantum walks (QWs) describe the evolution of quantum systems on graphs. An intrinsic degree of freedom---called the coin and represented by a finite-dimensional Hilbert space---is associated to each node. Scalar quantum walks are QWs with a one-dimensional coin. We propose a general strategy allowing one to construct scalar QWs on a broad variety of graphs, which admit embedding in Eulidean spaces, thus having a direct geometric interpretation. After reviewing the technique that allows one to regroup cells of nodes into new nodes, transforming finite spatial blocks into internal degrees of freedom, we prove that no QW with a two-dimensional coin can be derived from an isotropic scalar QW in this way. Finally we show that the Weyl and Dirac QWs can be derived from scalar QWs in spaces of dimension up to three, via our construction.Comment: 22 pages, 2 figure

Isotropic quantum walks on lattices and the Weyl equation

We present a thorough classification of the isotropic quantum walks on lattices of dimension $d=1,2,3$ for cell dimension $s=2$. For $d=3$ there exist two isotropic walks, namely the Weyl quantum walks presented in Ref. [G. M. D'Ariano and P. Perinotti, Phys. Rev. A 90, 062106 (2014)], resulting in the derivation of the Weyl equation from informational principles. The present analysis, via a crucial use of isotropy, is significantly shorter and avoids a superfluous technical assumption, making the result completely general.Comment: 16 pages, 1 figur

The Italian expenditure in transport infrastructure: a survey

The aim of the paper is to analyse the most important quantitative data on Italian expenditures in transport infrastructures (investment and maintenance costs), linking the expenditure with traffic flows. The analysis concerns rail and road networks (both for national and local roads), over the last ten years, and a possible forecast for the next years, thanks to the official previsions of the “Objective Law”. The whole analysis is based on official data. The planned infrastructures will analyzed with taxonomical and cost – benefit approaches, in order to provide a ranking of priority. The results show how the planning of the investment expenditure is still based on different criteria than efficiency. So, the foreseen expenditure will not able to give relevant effects in order to improve the efficiency of the transport system and to obtain better allocative issues.transport expenditure; italy; infrastructure; investment

Classical theories with entanglement

We investigate operational probabilistic theories where the pure states of every system are the vertices of a simplex. A special case of such theories is that of classical theories, i.e. simplicial theories whose pure states are jointly perfectly discriminable. The usual Classical Theory satisfies also local discriminability. However, simplicial theories---including the classical ones---can violate local discriminability, thus admitting of entangled states. First, we prove sufficient conditions for the presence of entangled states in arbitrary probabilistic theories. Then, we prove that simplicial theories are necessarily causal, and this represents a no-go theorem for conceiving non-causal classical theories. We then provide necessary and sufficient conditions for simplicial theories to exhibit entanglement, and classify their system-composition rules. We conclude proving that, in simplicial theories, an operational formulation of the superposition principle cannot be satisfied, and that---under the hypothesis of $n$-local discriminability---no mixed state admits of a purification. Our results hold also in the general case where the sets of states fail to be convex.Comment: The definitions of simplicial and classical theories have been relaxed, in order to include the non-convex cases; the results hold also in the non-convex cases. Improved and extended presentation. Added results on superposition and purification. Enhanced the 'Discussion and Conclusions' section. Minor corrections. Layout fixed and mention to Ref. [13] correcte

A high performance home in the Mediterranean climate: From the design principle to actual measurements

Experience developed in the northern European countries led, in the last decades, to standard and shared procedures for the design and construction of passive houses and similar high performance buildings. These approaches are specifically developed for cold climates, therefore cannot be directly applied to the Mediterranean climate, where substantially different climatic conditions must be challenged. The design and early monitoring of a customized zero energy house, located in Sicily, is proposed as an exemplary case study for the future generation of high performance and nearly-zero energy buildings in the Mediterranean area. The key role played by the control of heat gains, and the correct use of thermal mass is highlighted, showing similarities and differences with passive houses built in the North Europe. The measurements of energy and environmental performance of the building show the effectiveness of the response of the adopted design approach to the specific climatic conditions

Measurement incompatibility is strictly stronger than disturbance

The core of Heisenberg's argument for the uncertainty principle, involving the famous $\gamma$-ray microscope $\textit{Gedankenexperiment}$, consists in the existence of measurements that irreversibly alter the state of the system on which they are acting, causing an irreducible disturbance on subsequent measurements. The argument was put forward to justify the existence of incompatible measurements, namely, measurements that cannot be performed jointly. In this Letter, on the one hand, we provide a compelling argument showing that incompatibility is indeed a sufficient condition for disturbance, while, on the other hand, we exhibit a toy theory that is a counterexample for the converse implication.Comment: 21 pages (5 main text + 16 supplemental material); no figures, lots of diagram

«Copiati esattissimamente in misura rigorosa»: note sulle prime incisioni dei dittici eburnei del Tesoro del Duomo di Monza. Anton Francesco Gori, Anton Francesco Frisi e i fratelli Trivulzio nella seconda metà del Settecento

The Treasury of Duomo of Monza preserves three famous ivory diptychs part of liturgical furnishings which belonged to Berengario of Friuli (10th century): diptych of Stilicho and diptych of the Poet and the Muse, both Late Antique, and diptych of King David and St. Gregory, more controversial in dating and interpretation (6th century and Carolingian Age). Anton Francesco Gori is the first editor of the diptychs: he published them into the second volume of Thesaurus veterum diptychorum consularium et ecclesiasticorum (1759), furnishing it with three plates by Andrea Scacciati. Although he never viewed them, the Florentine erudite focuses on a wide critical examination of the artefacts based mainly on the watercolours painted by Girolamo Ferroni, who was hired by the Milanese marquis and precious mediator Alessandro Teodoro Trivulzio. In 1794, the canon Anton Francesco Frisi, who is considered the father of Monza’s historiography, decides to re-edit the diptychs in the third volume’s opening of his Memorie storiche di Monza e sua corte. Advised by don Carlo Trivulzio, erudite and owner of a rich unit of ancient ivories and supported by Giulio Cesare Bianchi’s humble engravings, Frisi offers a reading which clarifies and partially confirms what Gori wrote before, reading that is mildly argumentative about «chi non ha esaminati personalmente i Monumenti, sui quali ragiona». Considering on the background the cultural context of the time and the personalities who got involved, alongside the help of the documents divided by Veneranda Biblioteca Ambrosiana in Milan, Fondazione Trivulzio Archives and Biblioteca Marucelliana in Florence, this paper aims to propose a reconstruction of the events, focusing on the connection between the original version (the diptychs) and the copy (drawings and etchings that followed).Nel Tesoro del Duomo di Monza si conservano tre celebri dittici eburnei relativi alla dotazione di suppellettili liturgiche di Berengario del Friuli (inizi X secolo): il dittico di Stilicone e quello del Poeta e della Musa, entrambi tardo antichi; il dittico di re Davide e san Gregorio Magno, di datazione e lettura più controverse (VI secolo ed età carolingia). Primo editore dei pezzi è Anton Francesco Gori nel secondo volume del Thesaurus veterum diptychorum consularium et ecclesiasticorum (1759), corredato di tre tavole di Andrea Scacciati. Pur non avendo mai visionato i manufatti, l’erudito fiorentino dedica ad essi un’ampia disamina critica basandosi essenzialmente sugli acquerelli del pittore Girolamo Ferroni, reclutato dal marchese milanese e prezioso intermediario Alessandro Teodoro Trivulzio. Nel 1794 il padre della storiografia monzese, il canonico Anton Francesco Frisi, risolve di rieditare i dittici in apertura del terzo tomo delle sue Memorie storiche di Monza e sua corte. Consigliato da quel don Carlo Trivulzio erudito e proprietario di un ricco nucleo di avori antichi, supportato dalle modeste incisioni di Giulio Cesare Bianchi, offre una rilettura che puntualizza ed emenda in parte quanto scritto dal Gori, condita da una vena polemica contro «chi non ha esaminati personalmente i Monumenti, sui quali ragiona». Sullo sfondo del contesto culturale dell’epoca e delle personalità che vi presero parte, con l’ausilio della documentazione divisa tra la Veneranda Biblioteca Ambrosiana di Milano, l’Archivio della Fondazione Trivulzio e la Biblioteca Marucelliana di Firenze, il contributo intende proporre una ricostruzione degli avvenimenti con attenzione al rapporto tra originale (i dittici monzesi) e copia (disegni e incisioni che ne scaturirono)