Is a stokes four-vector like (1 1 0 0) being horizontal polarized vector can be treated as a quantum state? If the answer is yes, this state can be used to construct density matrix?
Yes and yes. http://en.wikipedia.org/wiki/Polarization_(waves) The coherency matrix is nothing else than a density matrix.
But coherency matrix is a 2χ2 matrix, which can be constructed by stokes parameters. The density matrix constructed by stokes vector itself would be a 4χ4 matrix. ρ=(1 1 0 0)χ(1 1 0 0) If this 4χ4 matrix is a density matrix, how can I measure the degree of polarization of this density matrix?
The Stokes vector has 4 real components. The coherency matrix is a 2x2 complex matrix built from the unity matrix and the 3 Pauli matricies. That also makes 4 free variables. You can easily construct the density matrix from the Stokes vector and vice versa. Born and Wolf's textbook has a pretty good chapter on that.