  A general two qubit system expressed in terms of the complete set of unit and
fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features
of this system. The well-known physical interpretations associated with the
relativistic Dirac equation involving the symmetry operations of time-reversal
T, charge conjugation C, parity P, and their products are reinterpreted here by
examining their action on the basic Bell states. The transformation properties
of the Bell basis states under these symmetry operations also reveal that C is
the only operator that does not mix the Bell states whereas all others do. In a
similar fashion, expressing the various logic gates introduced in the subject
of quantum computers in terms of the Dirac matrices shows for example, that the
NOT gate is related to the product of time-reversal and parity operators.
