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.
Highlights
Photons, with information encoded in continuous-variable degrees of freedom, can travel great distance without significant decoherence
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
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
Summary
With information encoded in continuous-variable degrees of freedom, can travel great distance without significant decoherence. The original distillation protocol, which is conditioned on detectors finding no photons, outputs a state that evolves toward a Gaussian. A continuous variable analog of entanglement pumping, the compact distillery scheme, has been proposed [43] This scheme requires storage of only two modes per location at any moment in time. The requirements for a quantum central limit theorem to be valid will be highlighted and discussed in great detail We remark that these techniques are closely related to those used to prove the extremality principle [45], which asserts that for entanglement measures satisfying very specific properties, Gaussian states have the least entanglement of all states with the same second moments
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