Seminar at SMU Delhi
November 18, 2015 (Wednesday) ,
3:30 PM at Webinar
K. R. Parthasarathy,
Indian Statistical Institute, Delhi Centre
Design of experiments in quantum statistics
Abstract of Talk
Statistics in experiments dealing with electrons, photons etc., is governed by non-commutative or quantum probability. Here we look at a finite level system where the set of all orthogonal projection operators in a complex finite dimensional Hilbert space is the set of all ''events''. A ''state'' of such a system is a positive operator $\rho$ of unit trace and the probability of an event $P$ in the state $\rho$ is equal to $Tr\, \rho P$. A ''measurement'' $M$ in such a system is a positive operator valued measure $x \mapsto M_x$ on a finite set $S$ and the probability that the measured ''value'' is equal to $x$ is $Tr\, \rho M_x$. If $\rho$ is an unknown state one has to infer the state from repeated applications of ''suitably chosen'' measurements. The choice of such measurements is a ''(quantum) design''. We shall describe a couple of examples of such designs and state some well known unsolved problems.