Physical Distance Between Quantum States

We propose a physical distance between two quantum states. Qualitatively different from existing distances for quantum states, for example, the Fubini-Study distance, the physical distance between two orthogonal quantum states can be very small. This allows us to discuss the dynamical divergence of two quantum states that are initially very close by physical distance and define quantum Lyapunov exponent. We are also able to use physical distance to define quantum chaos measure, which can lead to quantum analogue of the classical Poincar\'e section. Three different systems, kicked rotor, three-site Bose-Hubbard model, and spin-1/2 XXZ model, are used to illustrate the physical distance.

PDF Abstract