The Monge distance between quantum states

  title={The Monge distance between quantum states},
  author={Karol Zyczkowski and Wojeciech S lomcz{\'y}nski},
We define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions ( Q-functions). This quantity fulfils the axioms of a metric and satisfies the followingsemiclassical property : the distance between two coherent states is equal to the Euclidean distance between corresponding points in the classical phase space. We compute analytically distances between certain states (coherent, squeezed, Fock and thermal) and discuss a scheme for numerical… CONTINUE READING