The separable mixed two-qubit X-states are classified in accordance with the degeneracies in the spectrum of density matrices. It is shown that there are four classes of separable X-states, among them: one four-dimensional family, a pair of two-dimensional families, and a single zero-dimensional maximally mixed state.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Yu and J. H. Eberly, “Evolution from entanglement to decoherence of bipartite mixed “X” states,” Quantum Inf. Comput., 7, 459–468 (2007).
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press (2011).
R. F. Werner, “Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model,” Phys. Rev. A, 40, No. 8, 4277–4281 (1989).
M. Horodecki and P. Horodecki, “Reduction criterion of separability and limits for a class of distillation protocols,” Phys. Rev. A, 59, 4206–4216 (1999).
S. Ishizaka and T. Hiroshima, “Maximally entangled mixed states under nonlocal unitary operations in two qubits,” Phys. Rev. A, 62, 22310 (2000).
F. Verstraete, K. Audenaert, T. D. Bie, and B. D. Moor, “Maximally entangled mixed states of two qubits,” Phys. Rev. A, 64, 012316 (2001).
N. Quesada, A. Al-Qasimi, and D. F. V. James, “Quantum properties and dynamics of X states,” J. Modern Optics, 59, 1322–1329 (2012).
P. Mendonca, M. Marchiolli, and D. Galetti, “Entanglement universality of two-qubit X-states,” Ann. Phys., 351, 79–103 (2014).
A. R. P. Rau, “Manipulating two-spin coherences and qubit pairs,” Phys. Rev. A, 61, 032301 (2000).
A. Peres, “Separability criterion for density matrices,” Phys. Rev. Lett., 77, 1413–1415 (1996).
V. Gerdt, A. Khvedelidze, and Yu. Palii, “On the ring of local polynomial invariants for a pair of entangled qubits,” Zap. Nauchn. Semin. POMI, 373, 104–123 (2009).
V. Gerdt, A. Khvedelidze, and Yu. Palii, “Constraints on SU(2)×SU(2) invariant polynomials for entangled qubit pair,” Phys. Atomic Nuclei, 74, 893–900 (2011).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 448, 2016, pp. 270–285.
Rights and permissions
About this article
Cite this article
Khvedelidze, A., Torosyan, A. The Spectrum and Separability of Mixed Two-Qubit X-States. J Math Sci 224, 349–359 (2017). https://doi.org/10.1007/s10958-017-3421-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-017-3421-5