Operator Schmidt ranks of bipartite unitary matrices

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Operator Schmidt ranks of bipartite unitary matrices. / Müller-Hermes, Alexander; Nechita, Ion.

In: Linear Algebra and Its Applications, Vol. 557, 2018, p. 174-187.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Müller-Hermes, A & Nechita, I 2018, 'Operator Schmidt ranks of bipartite unitary matrices', Linear Algebra and Its Applications, vol. 557, pp. 174-187. https://doi.org/10.1016/j.laa.2018.07.018

APA

Müller-Hermes, A., & Nechita, I. (2018). Operator Schmidt ranks of bipartite unitary matrices. Linear Algebra and Its Applications, 557, 174-187. https://doi.org/10.1016/j.laa.2018.07.018

Vancouver

Müller-Hermes A, Nechita I. Operator Schmidt ranks of bipartite unitary matrices. Linear Algebra and Its Applications. 2018;557:174-187. https://doi.org/10.1016/j.laa.2018.07.018

Author

Müller-Hermes, Alexander ; Nechita, Ion. / Operator Schmidt ranks of bipartite unitary matrices. In: Linear Algebra and Its Applications. 2018 ; Vol. 557. pp. 174-187.

Bibtex

@article{3be1be71aa414a7a990a3d6733a84d1d,
title = "Operator Schmidt ranks of bipartite unitary matrices",
abstract = "The operator Schmidt rank of an operator acting on the tensor product Cn⊗Cm is the number of terms in a decomposition of the operator as a sum of simple tensors with factors forming orthogonal families in their respective matrix algebras. It has been known that for unitary operators acting on two copies of C2, the operator Schmidt rank can only take the values 1, 2, and 4, the value 3 being forbidden. In this paper, we settle an open question, showing that the above obstruction is the only one occurring. We do so by constructing explicit examples of bipartite unitary operators of all possible operator Schmidt ranks, for arbitrary dimensions (n,m)≠(2,2).",
keywords = "Matrix realignment, Operator Schmidt rank, Tensor product, Unitary matrices",
author = "Alexander M{\"u}ller-Hermes and Ion Nechita",
year = "2018",
doi = "10.1016/j.laa.2018.07.018",
language = "English",
volume = "557",
pages = "174--187",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Operator Schmidt ranks of bipartite unitary matrices

AU - Müller-Hermes, Alexander

AU - Nechita, Ion

PY - 2018

Y1 - 2018

N2 - The operator Schmidt rank of an operator acting on the tensor product Cn⊗Cm is the number of terms in a decomposition of the operator as a sum of simple tensors with factors forming orthogonal families in their respective matrix algebras. It has been known that for unitary operators acting on two copies of C2, the operator Schmidt rank can only take the values 1, 2, and 4, the value 3 being forbidden. In this paper, we settle an open question, showing that the above obstruction is the only one occurring. We do so by constructing explicit examples of bipartite unitary operators of all possible operator Schmidt ranks, for arbitrary dimensions (n,m)≠(2,2).

AB - The operator Schmidt rank of an operator acting on the tensor product Cn⊗Cm is the number of terms in a decomposition of the operator as a sum of simple tensors with factors forming orthogonal families in their respective matrix algebras. It has been known that for unitary operators acting on two copies of C2, the operator Schmidt rank can only take the values 1, 2, and 4, the value 3 being forbidden. In this paper, we settle an open question, showing that the above obstruction is the only one occurring. We do so by constructing explicit examples of bipartite unitary operators of all possible operator Schmidt ranks, for arbitrary dimensions (n,m)≠(2,2).

KW - Matrix realignment

KW - Operator Schmidt rank

KW - Tensor product

KW - Unitary matrices

UR - http://www.scopus.com/inward/record.url?scp=85050658872&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2018.07.018

DO - 10.1016/j.laa.2018.07.018

M3 - Journal article

AN - SCOPUS:85050658872

VL - 557

SP - 174

EP - 187

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

ID: 203518999