On Tuesday, May 29, at 3 p.m., Alexandru Baltag (ILLC) and Jort Bergfeld (ILLC) will give a talk at the LIRa seminar: The “Quantum Paradise”: (Second-Order) Quantum Logic is Decidable! The talk will take place in Science Park, Room A1.04. Please find the abstract below.
We present (and briefly motivate) a family of dynamic logics of quantum programs (LQP) [introduced by Baltag and Smets]. We provide a decidability proof for these logics over finitely many “qubits” (i.e. with respect to the class of finite-dimensional Hilbert spaces). The proof method is based on extending an idea used by Dunn, Hagge, Moss, and Wang in their decidability proof for standard (propositional) quantum logic (over finite-dimensional spaces). Our revised technique is general enough to be applied to an even wider range of quantum logics: indeed, in the second part of the talk we extend our decidability result to Quantified Dynamic Quantum Logics (obtained by adding quantifiers over propositions and actions), and even to a version of Second-Order Quantum Logic! This presentation is based on joint work of the speakers with Sonja Smets and Kohei Kishida (as well as on-going work with them and Shengyang Zhong).