On the Ring of Local Unitary Invariants for Mixed X-States of Two Qubits

Gerdt Vladimir; Khvedelidze A; Palii Iurie

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GERDT, Vladimir, KHVEDELIDZE, A, PALII, Iurie. On the Ring of Local Unitary Invariants for Mixed X-States of Two Qubits. In: Journal of Mathematical Sciences (United States), 2017, nr. 2(224), pp. 238-249. ISSN 1072-3374. DOI: https://doi.org/10.1007/s10958-017-3409-1

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Journal of Mathematical Sciences (United States)

Numărul 2(224) / 2017 / ISSN 1072-3374 /ISSNe 1573-8795

On the Ring of Local Unitary Invariants for Mixed X-States of Two Qubits

DOI:https://doi.org/10.1007/s10958-017-3409-1

Pag. 238-249

Gerdt Vladimir¹, Khvedelidze A²³⁴, Palii Iurie⁵

¹ Joint Institute of Nuclear Research,
² Georgian Technical University,
³ Ivane Javakhishvili Tbilisi State University,
⁴ National Research Nuclear University MEPhI, Moscow,
⁵ Institute of Applied Physics, Academy of Sciences of Moldova

Disponibil în IBN: 18 februarie 2018

Rezumat

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.