Monge Distance between Quantum States

Physics – Quantum Physics

Scientific paper

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9 pages in LaTex - RevTex + 2 figures in ps. submitted to Phys. Rev. A

Scientific paper

10.1088/0305-4470/31/45/009

We define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q--functions). This quantity fulfills the axioms of a metric and satisfies the following semiclassical 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 computation of Monge distance for two arbitrary quantum states.

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