Universiteit Utrecht

Department of Mathematics


Strange convergence rates for estimation of the parameters of a quantum coin toss



Richard Gill (UU), March, 2004

The physics literature recently reported unusual convergence rates, namely N to the minus one quarter, and N to the minus three quarters, for (essentially) the mean squared error of two standard estimators of the state of a two level quantum system. This problem is the quantum analogue of the classical statistical problem of estimating the parameter p, given N outcomes of Bernoulli(p) trials. The better of the two estimators was a maximum likelihood estimator. I'll explain these rates and relate them to the quantum statistical geometry of the unit ball - the parameter space for this problem, replacing the unit interval of a classical coin toss. It seems that a 1/N rate is achievable using an adaptive estimation scheme. The work is joint with Manuel Ballester.


Back to the history of the seminar or the Colloquium Stochastiek homepage.
Budhi Arta Surya (surya@math.uu.nl)