Discrete Quantum Causal Dynamics

          @misc{ pirsa_PIRSA:09060029,
            doi = {10.48660/09060029},
            url = {https://pirsa.org/09060029},
            author = {Panangaden, Prakash},
            keywords = {Quantum Information, Quantum Foundations},
            language = {en},
            title = {Discrete Quantum Causal Dynamics},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {jun},
            note = {PIRSA:09060029 see, \url{https://pirsa.org}}
          }
          

Abstract

We give a mathematical framework to describe the evolution of quantum systems subject to finitely many interactions with classical apparatuus and with each other. The systems in question may be composed of distinct, spatially separated subsystems which evolve independently, but may also interact. The evolution is coded in a mathematical structure in such a way that the properties of causality, covariance and entanglement are faithfully represented. The key to this scheme is to use a special family of spacelike slices -- we call them locative -- that are not so large as to permit acausal influences but large enough to capture nonlocal correlations. I will briefly describe how the dynamics can be described as a functor to a suitable category of Hilbert spaces and will also give some connections with logic.