THE MONGE DISTANCE BETWEEN QUANTUM STATES

We define a metric in the space of quantum states taking the Monge dis tance between corresponding Husimi distributions (e-functions). This q uantity fulfils the axioms of a metric and satisfies the following sem iclassical property: the distance between two coherent states is equal to the Euclidean distance between corresponding points in the classic al phase space. We compute analytically distances between certain stat es (coherent, squeezed, Fock and thermal) and discuss a scheme for num erical computation of Monge distance for two arbitrary quantum states.