A discrete local invariant for quantum gates
L. Koponen, Ville Bergholm, Martti M. Salomaa · Quantum Information and Computation · 2006
In this paper we study the properties of two-qubit gates. We review the most common parameterizations for the local equivalence classes of two-qubit gates and the connections between them. We then introduce a new discrete local invariant, namely the number of local degrees of freedom that a gate can bind. The value of this invariant is calculated analytically for all the local equivalence classes of two-qubit gates. We find that almost all two-qubit gates can bind the full six local degrees of freedom and are in this sense more effective than the controlled-NOT gate which only can bind four local degrees of freedom.