Universal Entanglement Distillation

2026-09-30

AI Summary

This study addresses the efficiency loss inherent in entanglement distillation of unknown bipartite quantum states. To overcome this limitation, the authors propose a universal adaptive protocol that integrates local operations and classical communication (LOCC) tomography, adaptive distillation, and a local robustness lemma. Theoretically, this work demonstrates that prior ignorance of the state incurs no asymptotic rate penalty, thereby establishing the optimal uniform distillation rate under worst-case scenarios. Furthermore, for fixed finite-dimensional systems, the proposed protocol achieves the optimal asymptotic distillation rate for arbitrary unknown states with vanishing error, attaining all achievable rates of distillable entanglement strictly below the theoretical limit. These results provide a rigorous foundation for efficient entanglement distillation without requiring prior knowledge of the underlying quantum states.

Abstract

We present a universal entanglement distillation protocol that asymptotically achieves the distillable entanglement of any unknown bipartite state in a fixed finite dimension. That is, its ebit yield attains every rate below the optimum that would be available if the state were known, with vanishing trace-distance error. Our approach combines tomography by local operations and classical communication with an adaptive distillation routine, using a local robustness lemma to control finite-sample estimation errors. We also characterize worst-case distillation from a family of states: the optimal uniform rate is the minimum distillable entanglement on the family's closure. These results show that ignorance of the state need not incur an asymptotic rate penalty.

Problem

• entanglement distillation
• unknown bipartite state
• universal protocol
• distillable entanglement
• asymptotic rate

Innovation

• Universal entanglement distillation
• LOCC tomography
• Adaptive distillation
• Local robustness lemma
• Worst-case distillation