Second-Order Asymptotics of Conversions of Distributions and Entangled States Based on Rayleigh-Normal Probability Distributions

Understand

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.