Entanglement purification protocol for a mixture of a pure entangled state and a pure product state

TL;DR

This paper introduces an entanglement purification protocol tailored for a specific mixture of pure entangled and pure product states, combining bisection and hashing methods to optimize entanglement extraction.

Contribution

It proposes a novel purification protocol for orthogonal mixed states, providing recursive formulas and numerical rate calculations for improved entanglement distillation.

Findings

Protocol successfully purifies mixed states into maximally entangled pairs.

Recursive formulas enable rate calculation for different state configurations.

Numerical analysis demonstrates the protocol's effectiveness.

Abstract

We present an entanglement purification protocol for a mixture of a pure entangled state and a pure product state, which are orthogonal to each other. The protocol is combination of bisection method and one-way hashing protocol. We give recursive formula for the rate of the protocol for different states, i.e. the number of maximally entangled two-qubit pairs obtained with the protocol per a single copy of the initial state. We also calculate numerically the rate for some states.