Continuous-variable entanglement distillation and non-commutative central limit theorems

TL;DR

This paper introduces a comprehensive framework for continuous-variable entanglement distillation that converts noisy states into Gaussian states, utilizing protocols linked to non-commutative central limit theorems, with implications for quantum repeaters.

Contribution

It develops a unified framework for entanglement distillation protocols and connects their convergence to new non-commutative central limit theorems, advancing quantum communication methods.

Findings

Protocols offer flexible trade-offs for success probability and memory.

Convergence analyzed through non-commutative central limit theorems.

Implications for quantum repeater efficiency and design.

Abstract

Entanglement distillation transforms weakly entangled noisy states into highly entangled states, a primitive to be used in quantum repeater schemes and other protocols designed for quantum communication and key distribution. In this work, we present a comprehensive framework for continuous-variable entanglement distillation schemes that convert noisy non-Gaussian states into Gaussian ones in many iterations of the protocol. Instances of these protocols include (a) the recursive-Gaussifier protocol, (b) the temporally-reordered recursive-Gaussifier protocol, and (c) the pumping-Gaussifier protocol. The flexibility of these protocols give rise to several beneficial trade-offs related to success probabilities or memory requirements, which that can be adjusted to reflect experimental demands. Despite these protocols involving measurements, we relate the convergence in this protocols to new instances of non-commutative central limit theorems, in a formalism that we lay out in great detail. Implications of the findings for quantum repeater schemes are discussed.