Geodesic
The spectrum and separability of mixed two-qubit $X$-states
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 270-285
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@article{ZNSL_2016_448_a18,
     author = {A. Khvedelidze and A. Torosyan},
     title = {The spectrum and separability of mixed two-qubit $X$-states},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {270--285},
     year = {2016},
     volume = {448},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a18/}
}
TY  - JOUR
AU  - A. Khvedelidze
AU  - A. Torosyan
TI  - The spectrum and separability of mixed two-qubit $X$-states
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2016
SP  - 270
EP  - 285
VL  - 448
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a18/
LA  - en
ID  - ZNSL_2016_448_a18
ER  - 
%0 Journal Article
%A A. Khvedelidze
%A A. Torosyan
%T The spectrum and separability of mixed two-qubit $X$-states
%J Zapiski Nauchnykh Seminarov POMI
%D 2016
%P 270-285
%V 448
%U http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a18/
%G en
%F ZNSL_2016_448_a18
A. Khvedelidze; A. Torosyan. The spectrum and separability of mixed two-qubit $X$-states. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Tome 448 (2016), pp. 270-285. http://geodesic.mathdoc.fr/item/ZNSL_2016_448_a18/

[1] T. Yu, J. H. Eberly, “Evolution from entanglement to decoherence of bipartite mixed ‘X’ states”, Quantum Inf. Comput., 7 (2007), 459–468 | MR | Zbl

[2] M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, 2011 | MR

[3] R. F. Werner, “Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model”, Phys. Rev. A, 40:8 (1989), 4277–4281 | DOI

[4] M. Horodecki, P. Horodecki, “Reduction criterion of separability and limits for a class of distillation protocols”, Phys. Rev. A, 59 (1999), 4206–4216 | DOI

[5] S. Ishizaka, T. Hiroshima, “Maximally entangled mixed states under nonlocal unitary operations in two qubits”, Phys. Rev. A, 62 (2000), 22310 | DOI | MR

[6] F. Verstraete, K. Audenaert, T. D. Bie, B. D. Moor, “Maximally entangled mixed states of two qubits”, Phys. Rev. A, 64 (2001), 012316 | DOI | MR

[7] N. Quesada, A. Al-Qasimi, D. F. V. James, “Quantum properties and dynamics of X states”, J. Modern Optics, 59 (2012), 1322–1329 | DOI

[8] P. Mendonca, M. Marchiolli, D. Galetti, “Entanglement universality of two-qubit $X$-states”, Ann. Phys., 351 (2014), 79–103 | DOI | MR

[9] A. R. P. Rau, “Manipulating two-spin coherences and qubit pairs”, Phys. Rev. A, 61 (2000), 032301 | DOI | MR

[10] A. Peres, “Separability criterion for density matrices”, Phys. Rev. Lett., 77 (1996), 1413–1415 | DOI | MR | Zbl

[11] V. Gerdt, A. Khvedelidze, Yu. Palii, “On the ring of local polynomial invariants for a pair of entangled qubits”, Zap. Nauchn. Semin. POMI, 373, 2009, 104–123 | MR

[12] V. Gerdt, A. Khvedelidze, Yu. Palii, “Constraints on $\mathrm{SU(2)\times SU}(2)$ invariant polynomials for entangled qubit pair”, Phys. Atomic Nuclei, 74 (2011), 893–900 | DOI