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arXiv · 1801.00986

Maximal lexicographic spectra and ranks for states with fixed uniform margins

Xin Li
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Abstract

We find the spectrum in maximal lexicographic order for quantum states $\rho_{AB}\in\mathcal{H}_A\otimes \mathcal{H}_B$ with margins $\rho_A=\frac{1}{n}I_n$ and $\rho_B=\frac{1}{m}I_m$ and discuss the construction of $\rho_{AB}$. By nonzero rectangular Kronecker coefficients, we give counterexamples for Klyachko's conjecture which says that a quantum state with maximal lexicographical spectrum has minimal rank among all states with given margins. Moreover, we show that quantum states with the maximal lexicographical spectrum are extreme points.

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Xin Li. 2018-01-03. Maximal lexicographic spectra and ranks for states with fixed uniform margins. https://arxiv.org/abs/1801.00986

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