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

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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 the recursive Gaussifier
protocol and the pumping Gaussifier protocol. The flexibility of these
protocols give rise to several beneficial trade-offs related to success
probabilities or memory requirements that can be adjusted to reflect
experimental specifics. Despite these protocols involving measurements, we
relate the convergence in this protocols to new instances of non-commutative
central limit theorems. Implications of the findings for quantum repeater
schemes are discussed.