Quantum Computation and Information Seminar 

19/06/2008, 15:00 — 16:00 — Room P4.35, Mathematics Building
Paolo Zanardi, U Southern California

Critical fidelities: the (quantum) information geometrical approach to phase transitions

The manifold of coupling constants parameterizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with the quantum , i.e. zero-temperature, phase transitions featured by the corresponding system. This approach, that can be extended to finite temperatures as well, provides a universal conceptual framework to study quantum critical phenomena which is differential-geometric and information-theoretic at the same time. In this talk I will discuss the basic of the approach and touch upon applications to different classes of systems.