The R'enyi entanglement entropy (REE) is an entanglement quantifier considered as a natural generalisation of the entanglement entropy. When it comes to stochastic local operations and classical communication (SLOCC), however, only a limited class of the REEs satisfy the monotonicity condition, while their statistical properties beyond mean values have not been fully investigated. Here, we establish a general condition that the probability distribution of the REE of any order obeys under SLOCC. The condition is obtained by introducing a family of entanglement monotones that contain the higher-order moments of the REEs. The contribution from the higher-order moments imposes a strict limitation on entanglement distillation via SLOCC. We find that the upper bound on success probabilities for entanglement distillation exponentially decreases as the amount of raised entanglement increases, which cannot be captured from the monotonicity of the REE. Based on the strong restriction on entanglement transformation under SLOCC, we design a new method to estimate entanglement in quantum many-body systems from experimentally observable quantities.

中文翻译：

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随机局部操纵下Rényi纠缠熵的条件

R'enyi纠缠熵（REE）是被认为是纠缠熵的自然概括的纠缠量词。但是，当涉及到随机本地操作和经典通信（SLOCC）时，只有一类有限的REE满足单调性条件，而它们的超出平均值的统计属性尚未得到充分研究。在这里，我们建立了一个一般条件，即在SLOCC下任何订单的REE的概率分布都服从。通过引入一个包含REEs高阶矩的纠缠单调族来获得该条件。来自高阶矩的贡献对通过SLOCC进行的纠缠蒸馏施加了严格的限制。我们发现纠缠蒸馏成功概率的上限随纠缠量的增加而呈指数下降，这不能从REE的单调性中捕获。基于SLOCC下对纠缠变换的严格限制，我们设计了一种新的方法，可以根据实验可观察到的量来估计量子多体系统中的纠缠。