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Hermitian tensor and quantum mixed state

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arxiv 1902.02640 v4 pith:MUATSD67 submitted 2019-02-05 quant-ph math-phmath.MPmath.RA

Hermitian tensor and quantum mixed state

classification quant-ph math-phmath.MPmath.RA
keywords hermitianquantumtensordecompositionmathcalmixedorderstate
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Quantum estimates for classical polynomial optimization

    math-ph 2026-07 conditional novelty 5.0

    A quantum-variational matrix method is proposed for bounding homogeneous polynomials, with converging numerical tensor-eigenvalue estimates and a new conjectured inequality for Biasi's resonant Hamiltonians.

  2. Higher Degree $t$-Hermitian Forms and Positivity-Preserving Contractions

    math.SP 2026-02 reject novelty 4.0

    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.