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Hermitian tensor and quantum mixed state
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Hermitian tensor and quantum mixed state
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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.
Forward citations
Cited by 2 Pith papers
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The paper proposes higher-degree t-Hermitian forms with an FFT-based spectral theory, but the core conjugation identity is inconsistent, so the central claims fail as stated.
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