= Entanglement distillation
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= Entanglement purification
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Entanglement distillation uses <local operations and classical communication> on many noisy <entangled states> to produce fewer high-fidelity <Bell pairs>. It is also called entanglement purification. The protocol may fail or abort; naming a purification step does not guarantee successful output for arbitrary inputs. If the output is an exact <pure state> of <Bell pairs>, every <purification of a density operator> factors between those pairs and the environment, so measuring each pair in the <computational basis> gives a shared uniform bit independent of an eavesdropper. Approximate privacy follows when the entire retained output is sufficiently close to that pure target. A <separable quantum state> cannot be distilled into a <Bell pair> by <LOCC>, because each local branch preserves separability.
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