Abstract
In this paper we study the properties of two-qubit gates. We review the most commonparameterizations for the 1o cal equivalence classes of two-qubit gates and the connectionsbetween them. We then introduce a new discrete local invariant, namely the number oflocal degrees of freedom that a gate can bind. The value of this invariant is calculatedanalitically for all the local equivalence classes of two-qubit gates. We find that almostall two-qubit gates can bind the full six local degrees of freedom and are in this sensemore effective than the controlled-NOT gate which only can bind four local degrees offreedom.
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