Universal quantum resource distillation via composite generalised quantum Stein's lemma

2026-05-14

AI Summary

Existing quantum resource distillation protocols rely on precise prior knowledge of the input states, rendering them impractical for scenarios involving unknown or imperfectly prepared states. This work proposes the first universal distillation scheme that operates without any prior information about the input states, within the framework of resource non-generating operations. It establishes, for the first time, that optimal distillation rates are achievable even with completely unknown i.i.d. input states. By extending the generalized quantum Stein lemma to composite hypothesis testing and integrating recent advances in one-shot quantum information theory with an improved blurring technique, the protocol achieves universally optimal entanglement distillation under non-entangling operations. The optimal rate is characterized by the regularized relative entropy, offering both robustness and broad applicability.

Abstract

The performance of quantum resource manipulation protocols, including key examples such as distillation of quantum entanglement, is measured in terms of the rate at which desired target states can be produced from a given noisy state. However, to achieve optimal rates, known protocols require precise tailoring to the quantum state in question, demanding a perfect knowledge of the input and allowing no errors in its preparation. Here we show that distillation of quantum resources in the framework of resource non-generating operations can be performed universally: optimal rates of distillation can be achieved with no knowledge of the input state whatsoever, certifying the robustness of quantum resource distillation. The findings apply in particular to the purification of quantum entanglement under non-entangling maps, where the optimal rates are governed by the regularised relative entropy of entanglement. Our result relies on an extension of the generalised quantum Stein's lemma in quantum hypothesis testing to a composite setting where the null hypothesis is no longer a fixed quantum state, but is rather composed of i.i.d. copies of an unknown state. The solution of this asymptotic problem is made possible through new developments in one-shot quantum information and a refinement of the blurring technique from [Lami, arXiv:2408.06410].

Problem

• quantum resource distillation
• universal protocols
• unknown input state
• optimal rates
• composite hypothesis testing

Innovation

• universal distillation
• composite quantum Stein's lemma
• resource non-generating operations
• regularised relative entropy
• one-shot quantum information