ALTERNATIVE DECOMPOSITION OF TWO-QUTRIT PURE STATES AND ITS RELATION WITH ENTANGLEMENT INVARIANTS

Based on maximally entangled states in the full- and sub-spaces of two-qutrits, we present an alternative decomposition of two-qutrit pure states in a form vertical bar Psi > = p(1)/root 3 (vertical bar 00 > + vertical bar 11 > + vertical bar 22 >) + p(2)/root 2 (vertical bar 01 > + vertical bar 12 >) + p(3)e(i theta)vertical bar 02 >. Similar to the Schmidt decomposition, all two-qutrit pure states can be transformed into the alternative decomposition under local unitary transformations, and the parameter p(1) is shown to be an entanglement invariant.