Geodesic
Conditions for the representability of the density matrix
Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 2, pp. 287-294

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The necessary and sufficient condition for the $N$-representability of reduced density matrices is found for functions of limited rank. 
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     author = {M. M. Mestechkin},
     title = {Conditions for the representability of the density matrix},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1969_1_2_a11/}
}
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M. M. Mestechkin. Conditions for the representability of the density matrix. Teoretičeskaâ i matematičeskaâ fizika, Tome 1 (1969) no. 2, pp. 287-294. http://geodesic.mathdoc.fr/item/TMF_1969_1_2_a11/