Hermitian tensor and quantum mixed state
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 sep...
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| Main Author: | |
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| Format: | Journal Article |
| Language: | English |
| Published: |
05-02-2019
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | 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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| DOI: | 10.48550/arxiv.1902.02640 |