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Oxford Quantum Talks Archive

States and measures

Andreas Doering, Imperial College London
Categories, Logic and Foundations of Physics V, August 2009, Imperial College London

The most general kind of a state of a classical system is a probability measure on the state space of the system. This also defines an integral on the abelian algebra of physical quantities. A general state of a quantum system is a positive linear functional of norm 1 on the nonabelian algebra of physical quantities of the quantum system., i.e., an integral. We will show that quantum states also have a description as probability measures. These measures are not defined on a state space (which does not exist anyway, due to the Kochen-Specker theorem), but on the spectral presheaf, a generalised state object in a topos associated to the quantum system.

[video] [streaming video]