Email this article On the Ring of Local Unitary Invariants for Mixed X-States of Two Qubits
- Authors: Gerdt V.1, Khvedelidze A.2,3,4, Palii Y.5
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Affiliations:
- Laboratory of Information Technologies, Joint Institute for Nuclear Research, University “Dubna”
- Institute of Quantum Physics and Engineering Technologies, Georgian Technical University
- A. Razmadze Mathematical Institute, Iv. Javakhishvili Tbilisi State University
- National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
- Institute of Applied Physics
- Issue: Vol 224, No 2 (2017)
- Pages: 238-249
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/239536
- DOI: https://doi.org/10.1007/s10958-017-3409-1
- ID: 239536
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Abstract
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.
About the authors
V. Gerdt
Laboratory of Information Technologies, Joint Institute for Nuclear Research, University “Dubna”
Author for correspondence.
Email: gerdt@jinr.ru
Russian Federation, Dubna
A. Khvedelidze
Institute of Quantum Physics and Engineering Technologies, Georgian Technical University; A. Razmadze Mathematical Institute, Iv. Javakhishvili Tbilisi State University; National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Email: gerdt@jinr.ru
Georgia, Tbilisi; Tbilisi; Moscow
Yu. Palii
Institute of Applied Physics
Email: gerdt@jinr.ru
Moldova, Republic of, Chisinau
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