Information is physical
Information theory can be considered as a branch of mathematics. But any actual processing, storing, or transmission of information must be carried out using concrete physical devices. Therefore, the way we handle information in concrete applications is constrained by the laws of physics. A simple example of this is the fact that, due to special relativity, we cannot transmit information faster than light. Of course, the ways in which the laws of physics constrain information transmission, storing, and processing, are mucho more involved, and its study constitutes a whole chapter in the history of physics. Nowadays, it is a major area of research in the foundations of quantum physics and gives place to the quest for informational axioms to singularize quantum theory among more general no-signal theories.
Our research
Quantum logic and generalized probabilistic models can be used to compare classical and quantum information theories, and classical and quantum computing. In particular, it is an open to determine what is the role of quantum logic in quantum computing, and whether there is a connection between the fact that quantum physics can be considered as a non-classical probability calculus on one hand, and quantum advantage on the other. We have explored on this idea, and studied the role played by contextuality in distinguishing universal vs non-universal sets of quantum gates. This study was recently extended to the study of different sets of quantum logical gates.
Our goals
Our goal is to understand what are the logical and algebraic structures underlying quantum computing and quantum information theory in general. In particular, to determine what is the role played by the quantum logical structure of quantum theory in quantum computing, and whether this plays any role in explaining why a quantum advantage should be expected. Also, it is relevant for us to understand the properties of different sets of quantum logical gates in terms of resource theories, and connect these properties with the problem of quantum advantage.
