PIRSA:13090068

Quantum Observables as Real-valued Functions and Quantum Probability

(2013). Quantum Observables as Real-valued Functions and Quantum Probability. Perimeter Institute. https://pirsa.org/13090068

Quantum Observables as Real-valued Functions and Quantum Probability. Perimeter Institute, Sep. 10, 2013, https://pirsa.org/13090068 

          @misc{ pirsa_PIRSA:13090068,
            doi = {10.48660/13090068},
            url = {https://pirsa.org/13090068},
            author = {},
            keywords = {Quantum Foundations},
            language = {en},
            title = { Quantum Observables as Real-valued Functions and Quantum Probability},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {sep},
            note = {PIRSA:13090068 see, \url{https://pirsa.org}}
          }
Talk number
PIRSA:13090068
Collection
Talk Type
Subject
Abstract
Quantum observables are commonly described by self-adjoint operators on a Hilbert space H. I will show that one can equivalently describe observables by real-valued functions on the set P(H) of projections, which we call q-observable functions. If one regards a quantum observable as a random variable, the corresponding q-observable function can be understood as a quantum quantile function, generalising the classical notion. I will briefly sketch how q-observable functions relate to the topos approach to quantum theory and the process called daseinisation. The topos approach provides a generalised state space for quantum systems that serves as a joint sample space for all quantum observables. This is joint work with Barry Dewitt.