Charting the Shape of Hilbert Space: A Bit of Quantum Foundations at PI

          @misc{ pirsa_PIRSA:08010004,
            doi = {10.48660/08010004},
            url = {https://pirsa.org/08010004},
            author = {Fuchs, Chris},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Charting the Shape of Hilbert Space:  A Bit of Quantum Foundations at PI},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {jan},
            note = {PIRSA:08010004 see, \url{https://pirsa.org}}
          }
          

Abstract

As physicists, we have become accustomed to the idea that a theory\\\'s content is always most transparent when written in coordinate-free language. But sometimes the choice of a good coordinate system is very useful for settling deep conceptual issues. Think of how Eddington-Finkelstein coordinates settled the longstanding question of whether the event horizon of a Schwarzschild black hole corresponds to a real spacetime singularity or not. Similarly we believe for an information-oriented or Bayesian approach to quantum foundations: That one good coordinate system may (eventually!) be worth more than a hundred blue-in-the-face arguments. This talk will motivate and chronicle the search for one such candidate coordinate system---the so-called Symmetric Informationally Complete Measurement---which has caught the attention of a handful of us here at PI and a handful of our visitors.