Quantum PT-Phase Diagram in a Non-Hermitian Photonic Structure

Photonic structures have an inherent advantage to realize PT-phase transition through modulating the refractive index or gain-loss. However, quantum PT properties of these photonic systems have not been comprehensively studied yet. Here, in a bi-photonic structure with loss and gain simultaneously existing, we analytically obtained the quantum PT-phase diagram under the steady state condition. To characterize the PT-symmetry or -broken phase, we define an Hermitian exchange operator expressing the exchange between quadrature variables of two modes. If inputting several-photon Fock states into a PT-broken bi-waveguide splitting system, most photons will concentrate in the dominant waveguide with some state distributions. Quantum PT-phase diagram paves the way to the quantum state engineering, quantum interferences, and logic operations in non-Hermitian photonic systems.Comment: 6 pages, 3 figure

Crisp bi-G\"{o}del modal logic and its paraconsistent expansion

In this paper, we provide a Hilbert-style axiomatisation for the crisp bi-G\"{o}del modal logic \KbiG. We prove its completeness w.r.t.\ crisp Kripke models where formulas at each state are evaluated over the standard bi-G\"{o}del algebra on $[0,1]$. We also consider a paraconsistent expansion of \KbiG with a De Morgan negation $\neg$ which we dub \KGsquare. We devise a Hilbert-style calculus for this logic and, as a~con\-se\-quence of a~conservative translation from \KbiG to \KGsquare, prove its completeness w.r.t.\ crisp Kripke models with two valuations over $[0,1]$ connected via $\neg$. For these two logics, we establish that their decidability and validity are $\mathsf{PSPACE}$-complete. We also study the semantical properties of \KbiG and \KGsquare. In particular, we show that Glivenko theorem holds only in finitely branching frames. We also explore the classes of formulas that define the same classes of frames both in $\mathbf{K}$ (the classical modal logic) and the crisp G\"{o}del modal logic \KG^c. We show that, among others, all Sahlqvist formulas and all formulas $\phi\rightarrow\chi$ where $\phi$ and $\chi$ are monotone, define the same classes of frames in $\mathbf{K}$ and \KG^c

Designing with Iontronic Logic Gates -- From a Single Polyelectrolyte Diode to Small Scale Integration

This article presents the implementation of on-chip iontronic circuits via small-scale integration of multiple ionic logic gates made of bi-polar polyelectrolyte diodes. These ionic circuits are analogous to solid-state electronic circuits, with ions as the charge carriers instead of electrons/holes. We experimentally characterize the responses of a single fluidic diode made of a junction of oppositely charged polyelectrolytes (i.e., anion and cation exchange membranes), with a similar underlying mechanism as a solid-state p- and n-type junction. This served to carry out pre-designed logical computations in various architectures by integrating multiple diode-based logic gates, where the electrical signal between the integrated gates was transmitted entirely through ions. The findings shed light on the limitations affecting the number of logic gates that can be integrated, the degradation of the electrical signal, their transient response, and the design rules that can improve the performance of iontronic circuits

A Heuristic Neural Network Structure Relying on Fuzzy Logic for Images Scoring

Traditional deep learning methods are sub-optimal in classifying ambiguity features, which often arise in noisy and hard to predict categories, especially, to distinguish semantic scoring. Semantic scoring, depending on semantic logic to implement evaluation, inevitably contains fuzzy description and misses some concepts, for example, the ambiguous relationship between normal and probably normal always presents unclear boundaries (normal − more likely normal - probably normal). Thus, human error is common when annotating images. Differing from existing methods that focus on modifying kernel structure of neural networks, this study proposes a dominant fuzzy fully connected layer (FFCL) for Breast Imaging Reporting and Data System (BI-RADS) scoring and validates the universality of this proposed structure. This proposed model aims to develop complementary properties of scoring for semantic paradigms, while constructing fuzzy rules based on analyzing human thought patterns, and to particularly reduce the influence of semantic conglutination. Specifically, this semantic-sensitive defuzzier layer projects features occupied by relative categories into semantic space, and a fuzzy decoder modifies probabilities of the last output layer referring to the global trend. Moreover, the ambiguous semantic space between two relative categories shrinks during the learning phases, as the positive and negative growth trends of one category appearing among its relatives were considered. We first used the Euclidean Distance (ED) to zoom in the distance between the real scores and the predicted scores, and then employed two sample t test method to evidence the advantage of the FFCL architecture. Extensive experimental results performed on the CBIS-DDSM dataset show that our FFCL structure can achieve superior performances for both triple and multiclass classification in BI-RADS scoring, outperforming the state-of-the-art methods

Logical Entropy: Introduction to Classical and Quantum Logical Information theory

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this paper is to give the direct generalization to quantum logical information theory that similarly focuses on the pairs of eigenstates distinguished by an observable, i.e., qudits of an observable. The fundamental theorem for quantum logical entropy and measurement establishes a direct quantitative connection between the increase in quantum logical entropy due to a projective measurement and the eigenstates that are distinguished by the measurement. Both the classical and quantum versions of logical entropy have simple interpretations as “two-draw” probabilities for distinctions. The conclusion is that quantum logical entropy is the simple and natural notion of information for quantum information theory focusing on the distinguishing of quantum states

Resource semantics: logic as a modelling technology

The Logic of Bunched Implications (BI) was introduced by O'Hearn and Pym. The original presentation of BI emphasised its role as a system for formal logic (broadly in the tradition of relevant logic) that has some interesting properties, combining a clean proof theory, including a categorical interpretation, with a simple truth-functional semantics. BI quickly found significant applications in program verification and program analysis, chiefly through a specific theory of BI that is commonly known as 'Separation Logic'. We survey the state of work in bunched logics - which, by now, is a quite large family of systems, including modal and epistemic logics and logics for layered graphs - in such a way as to organize the ideas into a coherent (semantic) picture with a strong interpretation in terms of resources. One such picture can be seen as deriving from an interpretation of BI's semantics in terms of resources, and this view provides a basis for a systematic interpretation of the family of bunched logics, including modal, epistemic, layered graph, and process-theoretic variants, in terms of resources. We explain the basic ideas of resource semantics, including comparisons with Linear Logic and ideas from economics and physics. We include discussions of BI's λ-calculus, of Separation Logic, and of an approach to distributed systems modelling based on resource semantics