The birth of a new logic
In a seminal paper published in 1936, Birkhoff and von Neumann realized that the propositions that one can do about a quantum system form a calculus which resembles that of classical logic. But the new logical connectives were different from the classical ones in a crucial aspect: the distributive law did not hold. They called Quantum Logic to this new propositional structure. One of the main implications is that one can view the probabilistic laws that govern quantum phenomena as a new form of probabilistic calculus, that is, as Quantum Probability.
Is quantum logic a logic?
Since the discovery of Quantum Logic, many other logical and algebraic structures were discovered in relation to the quantum formalism. These discoveries gave place to a prolific field of research which is called Quantum Structures. One of the main questions is: up to which point the new logical structures can be considered legitimate logics?
What can we do about that?
I was always fascinated by the idea that logic could be different. Put in other words: Why classical logic is as it is and not otherwise? Independently of the fact that it is very difficult to find an answer to that deep philosophical question, the truth is that Quantum Structures constitute a fascinating field of interdisciplinary research, which lies at the intersection of Physics, Logic, and Mathematics. You can find some of my works related to Quantum Logic & Quantum Probability in this link.
What is the logic underlying Quantum Computing?
The advent of the NISQ era poses a challenging question: What is the connection between the old Quantum Logical approach and the logic of Quantum Computing? This question has inspired a great part of my research during the last years. Currently, I am the Director of the Research Project Logical And Algebraic Structures Related To Quantum Information Processing, which is inspired by that question. In this paper I give an introductory idea about the fascinating philosophical and technical questions that motivate this research project.
