Abstract
The staggered model is a recent, very general variant of discrete-time quantum walks which, avoiding the use of a coin to direct the walker evolution, explores the underlying graph structure to build an evolution operator based on local unitaries induced by adjacent vertices. Optimising their implementation to increase resilience to decoherence phenomena motivates their analysis with the ZX-calculus. The whole optimisation can be seen as a graph reconfiguration process along which the original circuit is rewrote, significantly reducing the number of (expensive) gates used. The exercise identified an underlying pattern leading to an alternative, potentially more efficient evolution operator.

Abstract
This paper introduces Paraconsistent Reactive Graphs, as an extension of Reactive graphs that incorporates paraconsistency into the ground edges to address vagueness and inconsistency within dynamic systems. By assigning pairs of truth values to ground edges, this framework captures the uncertainty and contradictions stemming from incomplete or conflicting information. We explore the semantics of these graphs and provide a practical example to illustrate the proposed approach.

Abstract

Abstract
Discerning between quantum and classical correlations is of great importance. Bell polytopes are well established as a fundamental tool for such a purpose. In this paper, we extend this line of inquiry by applying resource theory within the context of network scenarios, to a Quantum Key Distribution (QKD) protocol, BBM92. To achieve this, we consider the causal structure P3 to describe the protocol, and we aim to develop useful statistical tests to assess it. Our objectives are twofold: firstly, to utilise the underlying causal structure of the QKD protocol to produce a geometrical analysis of the resulting nonconvex polytope, with a focus on the classical behaviours, and secondly to devise a test within this framework to evaluate the distance between any two behaviours within the generated polytope. This approach offers a unique perspective, linking deviations from expected behaviour directly to the quality of the quantum resource involved or the residual nonclassicality in protocol execution.

Abstract

Abstract
Kleene algebras (KA) and Kleene algebras with tests (KAT) provide an algebraic framework to capture the behavior of conventional programming constructs. This paper explores a broader understanding of these structures, in order to enable the expression of programs and tests yielding vague or inconsistent outcomes. Within this context, we introduce the concept of a paraconsistent Kleene Algebra with tests (PKAT), capable of capturing vague and contradictory computations. Finally, to establish the semantics of such a structure, we introduce two algebras, SetP(T) and RelP(K,T), parametric on a class of twisted structures K and T. We believe this sort of structures, for their huge flexibility, have an interesting application potential.