Entangling capacity of operators

Given a unitary operator U acting on a composite quantum system what is the entangling capacity of U? This question is investigated using a geometric approach. The entangling capacity, defined via metrics on the unitary groups, leads to a minimax problem. The dual, a maximin problem, is investigated in parallel and yields some familiar entanglement measures. A class of entangling operators, called generalized control operators is defined. The entangling capacities and other properties for this class of operators is studied.