# Rui Soares BarbosaInternational Iberian Nanotechnology Laboratory

Rui Soares Barbosa

BSc (Minho), MSc (Oxford), DPhil (Oxford)

Researcher at INL – International Iberian Nanotechnology Laboratory

## About

22

Publications

2,366

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325

Citations

Introduction

My interests lie at the intersection of Computer Science, Physics, and Mathematics. Broadly speaking, my research addresses interrelated questions on quantum foundations, quantum computer science, and the mathematics of quantum theory, with an emphasis on logical, structural, and compositional aspects.
More info: https://www.cs.ox.ac.uk/people/rui.soaresbarbosa/rsb

Additional affiliations

February 2020 - present

August 2019 - January 2020

August 2016 - December 2016

Education

October 2010 - July 2015

October 2009 - September 2010

February 2009 - June 2009

## Publications

Publications (22)

Contextuality is a non-classical behaviour that can be exhibited by quantum systems. It is increasingly studied for its relationship to quantum-over-classical advantages in informatic tasks. To date, it has largely been studied in discrete-variable scenarios, where observables take values in discrete and usually finite sets. Practically, on the oth...

Based on the connection between the categorical derivation of classical programs from specifications and a category-theoretic approach to quantum information, this paper contributes to extending the laws of classical program algebra to quantum programming. This aims at building correct-by-construction quantum circuits to be deployed on quantum devi...

Every small monoidal category with universal (finite) joins of central idempotents is monoidally equivalent to the category of global sections of a sheaf of (sub)local monoidal categories on a topological space. Every small stiff monoidal category monoidally embeds into such a category of global sections. These representation results are functorial...

This chapter contains an exposition of the sheaf-theoretic framework for contextuality emphasising resource-theoretic aspects, as well as some original results on this topic. In particular, we consider functions that transform empirical models on a scenario S to empirical models on another scenario T, and characterise those that are induced by clas...

Contextuality is a key signature of quantum non-classicality, which has been shown to play a central role in enabling quantum advantage for a wide range of information-processing and computational tasks. We study the logic of contextuality from a structural point of view, in the setting of partial Boolean algebras introduced by Kochen and Specker i...

Based on the connection between the categorical derivation of classical programs from specifications and the category-theoretic approach to quantum physics, this paper contributes to extending the laws of classical program algebra to quantum programming. This aims at building correct-by-construction quantum circuits to be deployed on quantum device...

Contextuality is a non-classical behaviour that can be exhibited by quantum systems. It is increasingly studied for its relationship to quantum-over-classical advantages in informatic tasks. To date, it has largely been studied in discrete variable scenarios, where observables take values in discrete and usually finite sets. Practically, on the oth...

We study simulation and quantum resources in the setting of the sheaf-theoretic approach to contextuality and non-locality. Resources are viewed behaviourally, as empirical models. In earlier work, a notion of morphism for these empirical models was proposed and studied. We generalize and simplify the earlier approach, by starting with a very simpl...

Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcome values; dually, states can be modelled as functions from the algebra of observables to outcome values. The probabilistic predictions of quantum physics are contextual in that they preclude this classical assum...

Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The probabilistic predictions of quantum physics are contextual in that they preclude this classical assumption of rea...

We analyse the minimum quantum resources needed to realise strong non-locality, as exemplified e.g. by the classical GHZ construction. It was already known that no two-qubit system, with any finite number of local measurements, can realise strong non-locality. For three-qubit systems, we show that strong non-locality can only be realised in the GHZ...

An important class of contextuality arguments in quantum foundations are the all-versus-nothing (AvN) proofs, generalizing a construction originally due to Mermin. We present a general formulation of AvN arguments and a complete characterization of all such arguments that arise from stabilizer states. We show that every AvN argument for an n -qubit...

We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of contextuality across measurement scenarios; it bears a precise relationship to violations of Bell inequalities; its v...

Homomorphisms between relational structures play a central role in finite model theory, constraint satisfaction and database theory. A central theme in quantum computation is to show how quantum resources can be used to gain advantage in information processing tasks. In particular, non-local games have been used to exhibit quantum advantage in bool...

We study the set of no-signalling empirical models on a measurement scenario, and show that the combinatorial structure of the no-signalling polytope is completely determined by the possibilistic information given by the support of the models. This is a special case of a general result which applies to all polytopes presented in a standard form, gi...

Contextuality is a key feature of quantum mechanics that provides an
important non-classical resource for quantum information and computation.
Abramsky and Brandenburger used sheaf theory to give a general treatment of
contextuality in quantum theory [New Journal of Physics 13 (2011) 113036].
However, contextual phenomena are found in other fields...

We explore a connection between monogamy of non-locality and a weak macroscopic locality condition: the locality of the average behaviour. These are revealed by our analysis as being two sides of the same coin.
Moreover, we exhibit a structural reason for both in the case of Bell-type multipartite scenarios, shedding light on but also generalising...

A notion of partial ideal for an operator algebra is a weakening the notion
of ideal where the defining algebraic conditions are enforced only in the
commutative subalgebras. We show that, in a von Neumann algebra, the
ultraweakly closed two-sided ideals, which we call total ideals, correspond to
the unitarily invariant partial ideals. The result a...

Extendability of an empirical model was shown by Abramsky & Brandenburger to
correspond in a unified manner to both locality and non-contextuality. We
develop their approach by presenting a refinement of the notion of
extendability that can also be useful in characterising the properties of
sub-models. The refinement is found to have another useful...

In a previous paper with Adam Brandenburger, we used sheaf theory to analyze
the structure of non-locality and contextuality. Moreover, on the basis of this
formulation, we showed that the phenomena of non-locality and contextuality can
be characterized precisely in terms of obstructions to the existence of global
sections.
Our aim in the present w...

The so-called topos approach provides a radical reformulation of quantum theory. Structurally, quantum theory in the topos formulation is very similar to classical physics. There is a state object, analogous to the state space of a classical system, and a quantity-value object, generalising the real numbers. Physical quantities are maps from the st...

## Questions

Question (1)

I know there's quite a bit of literature on acyclicity (particularly motivated by the theory of relational databases), but acyclicity is usually defined via e.g. the Graham reduction process or cycles in associated graphs, instead of being defined directly in terms of cycles on hypergraphs. I was able to find the following article:

Jégoua & Ndiaye, "On the notion of cycles in hypergraphs"

which provides a notion of cycles on hypergraphs such that "acyclicity" actually means "no cycles".

My (rather vague) question is whether this, or a similar, notion of cycle has been studied further. In particular, there seem to be different kinds of cycles. For example, if V = {v_0,...,v_n}, we could have a rather graph-like cycle:

{v_0,v_1}, {v_1,v_2}, ... , {v_i,v_(i+1)}, ..., {v_n,v_0}

or, in the opposite extreme, we could have a very tight kind of cycle if we think of the hypergraph whose hyperedges are all the sets of vertices of size n-1 [in other words, it corresponds to the boundary of the n-simplex]. I wonder if these different kinds of cycles have been studied somewhere in the literature (?).