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Open Quantum Systems Decoherence

Inertia of partial transpose of positive semidefinite matrices

arXiv
Authors: Yixuan Liang, Jiahao Yan, Dongran Si, Lin Chen

Year

2023

Paper ID

57233

Status

Preprint

Abstract Read

~2 min

Abstract Words

56

Citations

N/A

Abstract

We show that the partial transpose of 9times 9 positive semidefinite matrices do not have inertia (4,1,4) and (3,2,4). It solves an open problem in "LINEAR AND MULTILINEAR ALGEBRA, Changchun Feng et al, 2022". We apply our results to construct some inertia, as well as present the list of all possible inertia of partial transpose of 12times 12 positive semidefinite matrices.

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  • This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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  • We show that the partial transpose of 9times 9 positive semidefinite matrices do not have inertia (4,1,4) and (3,2,4).

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2310.16567 [2] arXiv https://arxiv.org/abs/2310.16567 [3] Publisher https://arxiv.org/abs/2310.16567

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