On quantitative determination of the degree of independence of qubit transformation by a quantum gate or channel

A multiqubit channel (quantum gate) is considered. A procedure of calculating the distance from the quantum-gate matrix to the subspace of matrices, which are tensor products of the transformation matrices of qubit subsystems, is proposed. The value of this distance indicates the degree of independence of transformation of these qubit subsystems. The proposed approach is considered as applied to waveguide implementation of quantum bits.