Hermitian tensor and quantum mixed state

Guyan Ni

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arXiv · 1902.02640

Hermitian tensor and quantum mixed state

Guyan Ni

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Abstract

An order $2m$ complex tensor $\cH$ is said to be Hermitian if \[\mathcal{H}_\ijm=\mathcal{H}_\jim ^*\mathrm{\ for\ all\ }\ijm .\] It can be regarded as an extension of Hermitian matrix to higher order. A Hermitian tensor is also seen as a representation of a quantum mixed state. Motivated by the separability discrimination of quantum states, we investigate properties of Hermitian tensors including: unitary similarity relation, partial traces, nonnegative Hermitian tensors, Hermitian eigenvalues, rank-one Hermitian decomposition and positive Hermitian decomposition, and their applications to quantum states.

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Guyan Ni. 2019-02-05. Hermitian tensor and quantum mixed state. https://arxiv.org/abs/1902.02640

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