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首页> 外文期刊>IEEE Transactions on Information Theory >Second-Order Asymptotics of Conversions of Distributions and Entangled States Based on Rayleigh-Normal Probability Distributions
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Second-Order Asymptotics of Conversions of Distributions and Entangled States Based on Rayleigh-Normal Probability Distributions

机译：基于瑞利-正态概率分布的分布和纠缠态的二阶渐近性

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摘要

We discuss the asymptotic behavior of conversions between two independent and identical distributions up to the second-order conversion rate when the conversion is produced by a deterministic function from the input probability space to the output probability space. To derive the second-order conversion rate, we introduce new probability distributions named Rayleigh-normal distributions. The family of Rayleigh-normal distributions includes a Rayleigh distribution and coincides with the standard normal distribution in the limit case. Using this family of probability distributions, we represent the asymptotic second-order rates for the distribution conversion. As an application, we also consider the asymptotic behavior of conversions between the multiple copies of two pure entangled states in quantum systems when only local operations and classical communications (LOCC) are allowed. This problem contains entanglement concentration, entanglement dilution, and a kind of cloning problem with LOCC restriction as special cases.
机译：我们讨论了当由确定性函数从输入概率空间到输出概率空间进行转换时，两个独立且相同的分布之间的转换的渐近行为，直到二阶转换率。为了得出二阶转换率，我们引入了称为瑞利正态分布的新概率分布。瑞利正态分布族包括瑞利分布，在极限情况下与标准正态分布一致。使用该概率分布族，我们表示分布转换的渐近二阶速率。作为一种应用，当仅允许本地操作和经典通信（LOCC）时，我们还考虑了量子系统中两个纯纠缠态的多个副本之间转换的渐近行为。此问题包含纠缠浓度，纠缠稀释度和特殊情况下具有LOCC限制的一种克隆问题。

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