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

TL;DR

This paper investigates the second-order asymptotics of distribution and entangled state conversions using Rayleigh-normal distributions, providing new insights into quantum information processing under LOCC constraints.

Contribution

It introduces Rayleigh-normal distributions to characterize second-order conversion rates and applies this framework to quantum entanglement transformations.

Findings

Derived second-order conversion rates for distribution transformations.

Introduced Rayleigh-normal distributions as a new probabilistic tool.

Analyzed asymptotic behavior of entangled state conversions under LOCC.

Abstract

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.