General relation between the transformation operator and an invariant under stochastic local operations and classical communication in quantum teleportation

In this paper, we introduce a transformation operator expression to give a criterion for faithful teleportation of an arbitrary two-qubit state via a four-qubit entangled state. The general relation between the transformation operator and the SLOCC invariant of quantum channel is obtained and its applicability is illuminated by some known examples for the measurement in the Bell basis.