QUANTUM-STATE SPACE METRIC AND CORRELATIONS

We study the Fubini-Study metric induced on the quantum evolution submanifold of the projective Hilbert space associated with the evolutions generated by a set of independent operators. It is shown that if the operators are Hermitian, then the off-diagonal components of the metric describe the correlations between them. Thus, not only the uncertainty but also the correlation acquires its geometrical interpretation. We also demonstrate this by using a squeezed state.