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Quantum Simulation Entanglement Theory Quantum Correlations

Linear rank preservers of tensor products of rank one matrices

arXiv

Authors: Zejun Huang, Shiyu Shi, Nung-Sing Sze

Year

2015

Paper ID

27483

Status

Preprint

Abstract Read

~2 min

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Abstract

Let n₁,ldots,n_k be integers larger than or equal to 2. We characterize linear maps φ: M_{n_1cdots n_k}→ M_{n_1cdots n_k} such that ${mathrm rank} $φ(A_1otimes cdots otimes A_k$)=1quadhbox{whenever}quad{mathrm rank} $A_1otimes cdots otimes A_k$=1 quad hbox{for all}quad A_i in M_{n_i}, i = 1,dots,k.$ Applying this result, we extend two recent results on linear maps that preserving the rank of special classes of matrices.

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This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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Let n1,ldots,nk be integers larger than or equal to 2.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1509.00541 [2] arXiv https://arxiv.org/abs/1509.00541 [3] Publisher https://arxiv.org/abs/1509.00541

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