One-Shot Non-Catalytic Distributed Purity Distillation

In this paper we revisit the problem of distributed purity distillation in the one-shot setting. The problem considers a bipartite quantum state ρ
^AB
shared between two parties Alice and Bob, who are allowed local unitary operations and one-way classical communication. The goal is to extract pure qubit states using these given resources, in their respective laboratories. A caveat of this problem is that all known protocols which recover the optimal number of pure qubit states require some pure qubits at the beginning at the protocol, to be used as ancilla. In this paper, we present a one-shot purity distillation protocol which requires a supply of ancilla qubits at 0 rate in the asymptotic iid setting, and little to no ancilla in the one-shot setting. We show that our protocol outperforms the best known purity distillation algorithms in terms of requirement of additional ancilla, while maintaining the same rate of pure states distilled.