On the distillablity conjecture in matrix theory

Saiqi Liu; Chen Lin

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arXiv · 2411.09527

On the distillablity conjecture in matrix theory

Saiqi Liu·Chen Lin

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Abstract

The distillability conjecture of two-copy 4 by 4 Werner states is one of the main open problems in quantum information. We prove two special cases of the conjecture. The first case occurs when two 4 by 4 matrices A, B are both unitarily equivalent to block diagonal matrices with 2 by 2 blocks. The second case occurs when B is unitarily equivalent to either -A or the transpose of -A. Plus, we propose a simplified version of the distillability conjecture when both A and B are matrices with distinct eigenvalues.

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Saiqi Liu, Chen Lin. 2024-11-14. On the distillablity conjecture in matrix theory. https://arxiv.org/abs/2411.09527

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