S. Ishizaka et T. Hiroshima, Maximally entangled mixed states under nonlocal unitary operations in two qubits - art. no. 022310, PHYS REV A, 6202(2), 2000, pp. 2310
We propose mixed states in two qubits that have a property that the amount
of entanglement of these states cannot be increased by any unitary transfor
mation. The property is proven when the rank of the states is less than 4,
and confirmed numerically in the other general cases. The corresponding ent
anglement of formation specified by its eigenvalues gives an upper bound of
that for density matrices with the same eigenvalues. Further, as a simple
application of the upper bound of the entanglement of formation, we analyze
the entanglement of formation of the state generated by a decohered contro
lled-NOT gate in the spin-boson model.