Quantum entangling power of adiabatically connected Hamiltonians

The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied.