A new local invariant for quantum gates

Koponen, Laura; Bergholm, Ville; Salomaa, Martti M.

A new local invariant for quantum gates

Authors

Koponen, Laura

Bergholm, Ville

Salomaa, Martti M.

Description

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.
8 pages, 2 figures