Informal seminar: "On the uncertainty and positivity of Wigner functions of one-dimensional mixed states"
Starts 25 Feb 2011 11:30
Ends 25 Feb 2011 20:00
Central European Time
Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
We present a new uncertainty relation for one-dimensional mixed states given its purity and degree of non-Gaussianity. This relation extends the purity-bounded uncertainty re
lation for mixed states derived by V. V. Dodonov and V. I. Man’ko. For the special case of pure states it provides us with an extended version of the Robertson-Schrödinger uncertainty relation, saturated by a set of states which includes all the eigenstates of the quantum harmonic oscillator. We represent our results as a bound in a three-dimensional parametric space of mixed states and identify the regions of the bound realized by states with non- negative Wigner function. This takes us closer to a proper extension of Hudson’s theorem to mixed states and permits us to visualize and compare the set of states with non-negative Wigner function and the set of states which minimize the newly derived uncertainty relation.