Publications
Partial orbits of quantum gates and full three-particle entanglement Vrije Universiteit Brussel
Quantum Probability: a reliable tool for an agent or a reliable source of reality? Vrije Universiteit Brussel
On the Connection Between Quantum Probability and Geometry Vrije Universiteit Brussel
underlie quantum probabilities. More
specifically, we explore possible connections
between logic, geometry and probability theory.
We propose an interpretation that generalizes the
method developed by R. T. Cox to the quantum log-
ical approach to physical theories. We stress the rel-
evance of developing a geometrical interpretation of
quantum mechanics.
...
States in generalized probabilistic models: an approach based in algebraic geometry Vrije Universiteit Brussel
We present a characterization of states in generalized probabilistic models by appealing to a non-commutative version of geometric probability theory based on algebraic geometry techniques. Our theoretical framework allows for incorporation of invariant states in a natural way.
Logical structures underlying quantum computing Vrije Universiteit Brussel
In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.
Dynamics of algebras in quantum unstable systems Vrije Universiteit Brussel
We introduce a dynamical evolution operator for dealing with unstable physical process, such as scattering resonances, photon emission, decoherence and particle decay. With that aim, we use the formalism of rigged Hilbert space and represent the time evolution of quantum observables in the Heisenberg picture, in such a way that time evolution is nonunitary. This allows to describe observables that are initially noncommutative, but become ...
Pattern Recognition in Non-Kolmogorovian Structures Vrije Universiteit Brussel
We present a generalization of the problem of pattern recognition to arbitrary probabilistic models. This version deals with the problem of recognizing an individual pattern among a family of different species or classes of objects which obey probabilistic laws which do not comply with Kolmogorov’s axioms. We show that such a scenario accommodates many important examples, and in particular, we provide a rigorous definition of the classical ...
Classical Limit and Quantum Logic Vrije Universiteit Brussel
The analysis of the classical limit of quantum mechanics usually focuses on the state of the system. The general idea is to explain the disappearance of the interference terms of quantum states appealing to the decoherence process induced by the environment. However, in these approaches it is not explained how the structure of quantum properties becomes classical. In this paper, we consider the classical limit from a different perspective. We ...
Lossless quantum data compression with exponential penalization Vrije Universiteit Brussel
Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum Rényi entropies. In order to do this, we appeal to a very general quantum encoding scheme that satisfies a quantum version of the Kraft-McMillan inequality. Then, in the standard situation, where one is intended to minimize the usual average length of the quantum codewords, we recover the known results, ...