On the distillablity conjecture in matrix theory
- URL: http://arxiv.org/abs/2411.09527v1
- Date: Thu, 14 Nov 2024 15:42:24 GMT
- Title: On the distillablity conjecture in matrix theory
- Abstract summary: 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.
- Score: 3.3222437269452887
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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