Computational geometry of positive definiteness

Huhtanen, Marko; Seiskari, Otto

doi:10.1016/j.laa.2012.05.002

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“…There are some algorithms that can be used to find positive definite Hermitian matrices within linear subspaces [19,20], however these Perron eigenvectors might be positive semidefinite.…”

Section: Introductionmentioning

confidence: 99%

Sinkhorn–Knopp theorem for PPT states

Cariello

2019

Lett Math Phys

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with tensor rank k, we provide an algorithm that checks whether the positive mapis equivalent to a doubly stochastic map. This procedure is based on the search for Perron eigenvectors of completely positive maps and unique solutions of, at most, k unconstrained quadratic minimization problems. As a corollary, we can check whether this state can be put in the filter normal form. This normal form is an important tool for studying quantum entanglement. An extension of this procedure to PPT states in M k ⊗ M m is also presented. √ k Id, D 1 = 1 √ m Id and tr(C i C j ) = tr(D i D j ) = 0, for every i = j [5, 6].

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“…There are some algorithms that can be used to find positive definite Hermitian matrices within linear subspaces [19,20], however these Perron eigenvectors might be positive semidefinite.…”

Section: Introductionmentioning

confidence: 99%