Discrete Phase Space and Minimum-Uncertainty States

          @misc{ scivideos_PIRSA:07030005,
            doi = {10.48660/07030005},
            url = {https://pirsa.org/07030005},
            author = {Wootters, William},
            keywords = {Quantum Information},
            language = {en},
            title = {Discrete Phase Space and Minimum-Uncertainty States},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2007},
            month = {mar},
            note = {PIRSA:07030005 see, \url{https://scivideos.org/index.php/pirsa/07030005}}
          }
          

Abstract

Consider a discrete quantum system with a d-dimensional state space. For certain values of d, there is an elegant information-theoretic uncertainty principle expressing the limitation on one's ability to simultaneously predict the outcome of each of d+1 mutually unbiased--or mutually conjugate--orthogonal measurements. (The allowed values of d include all powers of primes, and at present it is not known whether any value of d is excluded.) In this talk I show how states that minimize uncertainty in this sense can be generated via a discrete phase space based on finite fields. I also discuss some numerically observed features of these minimum-uncertainty states as the dimension d gets very large.