URL: http://eprints.ucm.es/43479/
1/T38970.pdf.
[CMHW18] M. Christandl, A. M¨uller-Hermes, and
M. M. Wolf. When Do Composed Maps
Become Entanglement Breaking? 2018.
arXiv:1807.01266.
[DHN19] G. De las Cuevas, M. Hoogsteder Riera,
and T. Netzer. Tensor decompositions
on simplicial complexes with invariance.
2019. arXiv:1909.01737.
[DN19] G. De las Cuevas and T. Netzer. Mixed
states in one spatial dimension: decom-
positions and correspondence with non-
negative matrices. 2019. arXiv:1907.
03664.
[DSPGC13] G. De las Cuevas, N. Schuch, D. Perez-
Garcia, and J. I. Cirac. Purifica-
tions of multipartite states: limitations
and constructive methods. New J.
Phys., 15:123021, 2013. doi:10.1088/
1367-2630/15/12/123021.
[FGP
+
15] H. Fawzi, J. Gouveia, P. A. Parrilo,
R. Z. Robinson, and R. R. Thomas.
Positive semidefinite rank. Math. Pro-
gram., 15:133, 2015. doi:10.1007/
s10107-015-0922-1.
[FMP
+
12] S. Fiorini, S. Massar, S. Pokutta,
H. R. Tiwary, and R. de Wolf. Lin-
ear vs. Semidefinite Extended Formu-
lations: Exponential Separation and
Strong Lower Bounds. STOC ’12 Proc.
of the 44th Symposium on Theory of
Computing, page 95, 2012. doi:10.
1145/2213977.2213988.
[FNT16] T. Fritz, T. Netzer, and A. Thom. Spec-
trahedral containment and operator sys-
tems with finite-dimensional realization.
SIAM J. Appl. Algebra Geom., 1:556,
2016. doi:10.1137/16M1100642.
[Gha10] S. Gharibian. Strong NP-Hardness of the
Quantum Separability Problem. Quan-
tum Inf. Comput., 10:343, 2010. arXiv:
0810.4507.
[Gie18] R. Gielerak. Schmidt decomposition of
mixed-pure states for (d,infty) systems
and some applications. 2018. arXiv:
1803.09541.
[GPT13] J. Gouveia, P. A. Parrilo, and R. R.
Thomas. Lifts of convex sets and cone
factorizations. Math. Oper. Res., 38:248,
2013. doi:10.1287/moor.1120.0575.
[Gur03] L. Gurvits. Classical deterministic com-
pleixty of Edmonds’ problem and quan-
tum entanglement. In STOC ’03: Proc.
of the 35th Annual ACM Symposium on
Theory of Computing, ACM, page 10,
2003. doi:10.1145/780542.780545.
[HHHH09] R. Horodecki, P. Horodecki,
M. Horodecki, and K. Horodecki.
Quantum entanglement. Rev.
Mod. Phys., 81:865, 2009. doi:
10.1103/RevModPhys.81.865.
[HKM13] J. W. Helton, I. Klep, and S. McCul-
lough. The matricial relaxation of a
linear matrix inequality. Math. Pro-
gram., 138:401, 2013. doi:10.1007/
s10107-012-0525-z.
[HLVC00] P. Horodecki, M. Lewenstein, G. Vi-
dal, and I. Cirac. Operational criterion
and constructive checks for the separa-
bility of low-rank density matrices. Phys.
Rev. A, 62:032310, 2000. doi:10.1103/
PhysRevA.62.032310.
[HSR03] M. Horodecki, P. W. Shor, and M. B.
Ruskai. Entanglement Breaking Chan-
nels. Rev. Math. Phys., 15:629, 2003.
doi:10.1142/S0129055X03001709.
[Jam72] A. Jamiolkowski. Linear transforma-
tions which preserve trace and posi-
tive semidefiniteness of operators. Rep.
Math. Phys., 3:9, 1972. doi:10.1016/
0034-4877(72)90011-0.
[Joh] N. Johnston.
http://www.njohnston.ca/2014/06/what-
the-operator-schmidt-decomposition-
tells-us-about-entanglement/.
[KCKL00] B. Kraus, J. I. Cirac, S. Karnas, and
M. Lewenstein. Separability in 2xN com-
posite quantum systems. Phys. Rev.
A, 61:062302, 2000. doi:10.1103/
PhysRevA.61.062302.
[KW03] K. Chen and L.-A. Wu. A matrix re-
alignment method for recognizing entan-
glement. Quantum Inf. Comput., 3:193,
2003. arXiv:0205017.
[LP15] M. Laurent and T. Piovesan. Conic ap-
proach to quantum graph parameters us-
ing linear optimization over the com-
pletely positive semidefinite cone. SIAM
J. Optim., 25:2461, 2015. doi:10.1137/
14097865X.
[NC00] M. A. Nielsen and I. L. Chuang. Quan-
tum Computation and Quantum Infor-
mation. Cambridge University Press,
2000. doi:10.1017/CBO9780511976667.
[Net19] T. Netzer. Free Semialgebraic Geometry.
2019. arXiv:1902.11170.
Accepted in Quantum 2019-10-31, click title to verify. Published under CC-BY 4.0. 13