arXiv subjects

Maria E. Stasinou

Publications and source records attributed to Maria E. Stasinou.

3 recordsLinked to original sources

arXiv2025

Generalised Process Theories

Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories (SMCs). However, various generalizations, including time-neutral, higher-order, and enriched process theories, do not naturally conform to this structure. In this work, we propose an alternative formalization using operad algebras, motivated by recent results connecting SMCs to operadic structures, which captures a broader class of process theories. By leveraging the string-diagrammatic language, we provide an accessible yet rigorous formulation that unifies and extends traditional process-theoretic approaches. Our operadic framework not only recovers standard process theories as a special case but also enables new insights into quantum foundations and compositional structures. This work paves the way for further investigations into the algebraic and operational properties of generalised process theories within an operadic setting.

math.CT↗

arXiv2024

Time symmetry in quantum theories and beyond

There exists a stark tension among different formulations of quantum theory as some are inherently time-symmetric while others are time-asymmetric. This tension is crisply captured when considering physical theories as theories of processes. We present the process theory of quantum physics, QPhys, which treats classical systems as internal to quantum theory. We provide three ways to incorporate time symmetry in QPhys. The first restricts the process theory of QPhys to one that satisfies an additional retrocausality constraint. The second is a novel approach, which extends the notions of causality and retrocausality to apply to systems along with processes. Utilizing this approach, we create a toy model for particle physics , where the causal and retrocausal systems correspond to particles and anti-particles respectively. The third approach extends QPhys to a supertheory that satisfies neither a causality nor a retrocausality constraint. To avoid unphysical predictions we modify either its composition rule or its processes.

quant-ph↗

arXiv2020

Functorial evolution of quantum fields

We present a compositional algebraic framework to describe the evolution of quantum fields in discretised spacetimes. We show how familiar notions from Relativity and quantum causality can be recovered in a purely order-theoretic way from the causal order of events in spacetime, with no direct mention of analysis or topology. We formulate theory-independent notions of fields over causal orders in a compositional, functorial way. We draw a strong connection to Algebraic Quantum Field Theory (AQFT), using a sheaf-theoretical approach in our definition of spaces of states over regions of spacetime. We introduce notions of symmetry and cellular automata, which we show to subsume existing definitions of Quantum Cellular Automata (QCA) from previous literature. Given the extreme flexibility of our constructions, we propose that our framework be used as the starting point for new developments in AQFT, QCA and more generally Quantum Field Theory.

quant-ph↗