Entangling properties of a mixed two-qubit system can be described by local homogeneous unitary invariant polynomials in the elements of the density matrix. The structure of the corresponding ring of invariant polynomials for a special subclass of states, the so-called mixed X-states, is established. It is shown that for the X-states there is an injective ring homomorphism of the quotient ring of SU(2)×SU(2)-invariant polynomials modulo its syzygy ideal to the SO(2) × SO(2)-invariant ring freely generated by five homogeneous polynomials of degrees 1, 1, 1, 2, 2.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 448, 2016, pp. 107–123.
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Gerdt, V., Khvedelidze, A. & Palii, Y. On the Ring of Local Unitary Invariants for Mixed X-States of Two Qubits. J Math Sci 224, 238–249 (2017). https://doi.org/10.1007/s10958-017-3409-1
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DOI: https://doi.org/10.1007/s10958-017-3409-1