ABSTRACT

Abstract We review some of the important properties of the states of qubit pairs. They are specified by 15 numerical parameters that are naturally regarded as the components of two 3-vectors and a 3 × 3dyadic. There are six classes of families of locally equivalent states in a straightforward scheme for classifying all 2-qubit states; four of the classes consist of two subclasses each. Easy-to-use criteria enable one to check whether a given pair of 3-vectors plus a 3× 3-dyadic specify a 2-qubit state; and if they do, whether the state is entangled; and if it is, whether it is a separable state. We remark on the Hill-Wootters concurrence, discuss the properties of the fundamental Lewenstein-Sanpera decompositions of 2-qubit states, and report a number of examples for which the optimal decomposition is known explicitly.