# Non-asymptotic entanglement distillation

## TL;DR

This paper investigates the fundamental limits of entanglement distillation in non-asymptotic scenarios, providing exact characterizations and computable estimates for the distillation rate under practical constraints.

## Contribution

It introduces a semidefinite program for one-shot distillable entanglement and derives second-order estimations for various quantum states, advancing understanding of non-asymptotic entanglement distillation.

## Key findings

- Exact characterization of one-shot distillable entanglement via quantum hypothesis testing relative entropy.
- Efficient second-order estimations of distillation rates for common quantum states.
- Explicit evaluations for pure, Bell mixture, maximally correlated, and isotropic states.

## Abstract

Entanglement distillation, an essential quantum information processing task, refers to the conversion from multiple copies of noisy entangled states to a smaller number of highly entangled states. In this work, we study the non-asymptotic fundamental limits for entanglement distillation. We investigate the optimal tradeoff between the distillation rate, the number of prepared states, and the error tolerance. First, we derive the one-shot distillable entanglement under completely positive partial transpose preserving operations as a semidefinite program and demonstrate an exact characterization via the quantum hypothesis testing relative entropy. Second, we establish efficiently computable second-order estimations of the distillation rate for general quantum states. In particular, we provide explicit as well as approximate evaluations for various quantum states of practical interest, including pure states, mixture of Bell states, maximally correlated states and isotropic states.

---
Source: https://tomesphere.com/paper/1706.06221