Abstract
Modelling complex information systems often entails the need for dealing with scenarios of inconsistency in which several requirements either reinforce or contradict each other. This lecture summarises recent joint work with Juliana Cunha, Alexandre Madeira and Ana Cruz on a variant of transition systems endowed with positive and negative accessibility relations, and a metric space over the lattice of truth values. Such structures are called paraconsistent transition systems, the qualifier stressing a connection to paraconsistent logic, a logic taking inconsistent information as potentially informative. A coalgebraic perspective on this family of structures is also discussed.

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.

Abstract
Secure Multiparty Computation (SMC) facilitates secure collaboration among multiple parties while safeguarding the privacy of their confidential data. This paper introduces a two-party quantum SMC protocol designed for evaluating binary Boolean functions using single qubits. Complexity analyses demonstrate a reduction of 66.7% in required quantum resources, achieved by utilizing single qubits instead of multi-particle entangled states. However, the quantum communication cost has increased by 40% due to the amplified exchange of qubits among participants. Furthermore, we bolster security by performing additional quantum operations along the y-axis of the Bloch sphere, effectively hiding the output from potential adversaries. We design the corresponding quantum circuit and implement the proposed protocol on the IBM Qiskit platform, yielding reliable outcomes.