Entanglement distillation in terms of a conjectured matrix inequality

Yize Sun; Lin Chen

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arXiv · 1909.02748

Entanglement distillation in terms of a conjectured matrix inequality

Yize Sun·Lin Chen

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Abstract

Entanglement distillation is a basic task in quantum information, and the distillable entanglement of three bipartite reduced density matrices from a tripartite pure state has been studied in [Phys. Rev. A 84, 012325 (2011)]. We extend this result to tripartite mixed states by studying a conjectured matrix inequality, namely $\mathop{\rm rank}(\sum_i R_i \otimes S_i)\leq K \mathop{\rm rank}(\sum_i R_i^T \otimes S_i)$ holds for any bipartite matrix $M=\sum_i R_i \otimes S_i$ and Schmidt rank $K$. We prove that the conjecture holds for $M$ with $K=3$ and some special $M$ with arbitrary $K$.

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Yize Sun, Lin Chen. 2019-09-06. Entanglement distillation in terms of a conjectured matrix inequality. https://arxiv.org/abs/1909.02748

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