Condensed Matter Physics, 2018, vol. 21, No. 3, 33003
Geometric measure of mixing of quantum state
(Department of Applied Physics and Nanomaterials Science, Lviv Polytechnic National University, 5 Ustiyanovych St., 79013 Lviv, Ukraine)
(Department for Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov St., 79005 Lviv, Ukraine)
We define the geometric measure of mixing of quantum state as a minimal Hilbert-Schmidt distance between the mixed state and a set of pure states. An explicit expression for the
geometric measure is obtained. It is interesting that this expression corresponds to the squared Euclidian distance between the mixed state and the pure one in space of eigenvalues
of the density matrix. As an example, geometric measure of mixing for spin-1/2 states is calculated.
mixed states, density matrix, Hilbert-Schmidt distance