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- W2943383140 abstract "In [M. Walter et al., Science 340, 1205, 7 June (2013)], they gave a sufficient condition for genuinely entangled pure states and discussed SLOCC classification via polytopes and the eigenvalues of the single-particle states. In this paper, for $4n$ qubits, we show the invariance of algebraic multiplicities (AMs) and geometric multiplicities (GMs) of eigenvalues and the invariance of sizes of Jordan blocks (JBs) of the coefficient matrices under SLOCC. We explore properties of spectra, eigenvectors, generalized eigenvectors, standard Jordan normal forms (SJNFs), and Jordan chains of the coefficient matrices. The properties and invariance permit a reduction of SLOCC classification of $4n$ qubits to integer partitions (in number theory) of the number $2^{2n}-k$ and the AMs." @default.
- W2943383140 created "2019-05-09" @default.
- W2943383140 creator A5022847585 @default.
- W2943383140 date "2019-05-05" @default.
- W2943383140 modified "2023-10-16" @default.
- W2943383140 title "Entanglement classification via integer partitions" @default.
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- W2943383140 doi "https://doi.org/10.48550/arxiv.1905.01751" @default.
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