Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MM_2014_26_11_a9, author = {A. M. Khvedelidze and I. A. Rogojin}, title = {On the separability problem for quantum composite systems}, journal = {Matemati\v{c}eskoe modelirovanie}, pages = {65--70}, publisher = {mathdoc}, volume = {26}, number = {11}, year = {2014}, language = {en}, url = {http://geodesic.mathdoc.fr/item/MM_2014_26_11_a9/} }
A. M. Khvedelidze; I. A. Rogojin. On the separability problem for quantum composite systems. Matematičeskoe modelirovanie, Tome 26 (2014) no. 11, pp. 65-70. http://geodesic.mathdoc.fr/item/MM_2014_26_11_a9/
[1] Schrodinger E., “Die gegenwartige situation in der quantenmechanik”, Naturwiss, 23 (1935), 807–812 | DOI
[2] Morozova E. A., Chentsov N. N., “Markov invariant geometry on manifolds of states”, Journal of Soviet Mathematics, 56:5 (1991), 2648–2669 | DOI | Zbl
[3] Dittmann J., “On the riemannian metric on the space of density matrices”, Reports on Mathematical Physics, 36:2 (1995), 309–315 | DOI | MR | Zbl
[4] Petz D., Sudar C., “Geometries of quantum states”, Journal of Mathematical Physics, 37 (1996), 2662–2673 | DOI | MR | Zbl
[5] Zyczkowski K., Horodecki P., Sanpera A., Lewenstein M., “On the volume of the set of mixed entangled states”, Phys. Rev., A58 (1998), 883 | DOI | MR
[6] Pittenger A. O., Rubin M. H., “Convexity and the separability problem of quantum mechanical density matrices”, Linear Algebra and its Applications, 346 (2002), 47–71 | DOI | MR | Zbl
[7] Gurvits L., “Classical deterministic complexity of Edmonds' problem and quantum entanglement”, STOC'03, ACM, New York, NY, USA, 2003, 10–19 | MR | Zbl
[8] Ioannou L. M., “Computational complexity of the quantum separability problem”, Quantum Info. Comput., 7 (2007), 335–370 | MR | Zbl
[9] Braunstein S. L., “Geometry of quantum inference”, Phys. Lett., A219 (1996), 189 | MR
[10] Physics A: Mathematical and General, 34 (2001), 7111–7125 | DOI | MR | Zbl
[11] Ginibre J., “Statistical ensembles of complex, quaternion, and real matrices”, Journal of Mathematical Physics, 6:3 (1965), 440–449 | DOI | MR | Zbl
[12] Bures D., “An extension of Kakutani's theorem on infinite product measures to the tensor product of semidefinite algebras”, Trans. Am. Mat. Soc., 135 (1969), 199 | MR | Zbl
[13] Braunstein S. L., Caves C. M., “Statistical distance and the geometry of quantum states”, Phys. Rev. Lett., 72 (1994), 3439–3443 | DOI | MR | Zbl
[14] Peres A., “Separability criterion for density matrices”, Phys. Rev. Lett., 77 (1996), 1413 | DOI | MR | Zbl
[15] Horodecki P., “Separability criterion and inseparable mixed states with positive partial transposition”, Phys. Lett., 232 (1977), 333 | DOI | MR
[16] Gerdt V., Khvedelidze A., Palii Y., “Constraints on $\mathrm{SU(2)}\otimes \mathrm{SU(2)}$ invariant polynomials for a pair of entangled qubits”, Physics of Atomic Nuclei, 74 (2011), 893–900 | DOI
[17] Gerdt V., Khvedelidze A., Mladenov D., Palii Y., “$\mathrm{SU(6)}$ casimir invariants and $\mathrm{SU(2)}\otimes \mathrm{SU(3)}$ scalars for a mixed qubit-qutrit state”, Journal of Mathematical Sciences, 179 (2011), 690–701 | DOI | MR
[18] Zyczkowski K., Sommers H. J., “Hilbert–Schmidt volume of the set of mixed quantum states”, Journal of Physics A: Mathematical and General, 36:39 (2003), 10115 | DOI | MR | Zbl
[19] Zyczkowski K., Sommers H. J., “Bures volume of the set of mixed quantum states”, Journal of Physics A: Mathematical and General, 36 (2003), 10083 | DOI | MR | Zbl
[20] Slater P. B., “Dyson indices and Hilbert–Schmidt separability functions and probabilities”, Journal of Physics A: Mathematical and General, 40 (2007), 14279 | DOI | MR | Zbl