Quantum Observables as Semispectral Measures - new problems with old questions

          @misc{ pirsa_PIRSA:06060050,
            doi = {10.48660/06060050},
            url = {https://pirsa.org/06060050},
            author = {Lahti, Pekka},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Quantum Observables as Semispectral Measures - new problems with old questions},
            publisher = {Perimeter Institute},
            year = {2006},
            month = {jun},
            note = {PIRSA:06060050 see, \url{https://pirsa.org}}
          }
          

Abstract

The modern view of representing a quantum observable as a semispectral measure as opposed to the traditional approach of using only spectral measures has added a great deal to our understanding of the mathematical structures and conceptual foundations of quantum mechanics. The old questions of 1) how to determine a quantum observable from its classical counter-part (if any), 2) how much statistical information is needed to determine an observable, 3) which observables can be measured together, and 4) are there noiseless measurements, all appear in a new perspective, calling for a study of problems such as: 1) how to obtain a semispectral measure by a quantization map, 2) do the moment operators of a semispectral measure determine the operator measure, 3) are coexistent observables jointly measurable, and 4) does minimal variance occur only in the case of a spectral measure? In my talk I will survey some of the recent developments concerning these questions and problems.