The many classical faces of quantum logic

Chris Heunen

Logic is crucial to the verification and design of algorithms and protocols. But in the case of quantum computer science, the appropriate logic remains mysterious. Quantum logic has to deal with overcoming counterintuitive phenomena. One such symptom is that standard (categorical) logic degenerates to modal logic in the quantum case. Luckily, logic also suggests a way out: much about a quantum system is captured by the collection of its classical subsystems. Hence quantum logic may be regarded as consisting of many classical faces. This leads to insights in the very foundations of quantum mechanics. I will survey this exciting development.