Entanglement Distillation
Distillation converts many weakly entangled or noisy pairs into fewer near-perfect Bell pairs using only local operations and communication.
Purifying a shared resource
Two distant parties often share entangled pairs degraded by noise. Distillation (also called purification) trades quantity for quality: starting from n copies of a noisy state, local operations and classical communication (LOCC) produce m < n pairs of much higher fidelity to a Bell state. The achievable ratio m/n in the large-n limit is the distillable entanglement, a fundamental measure of the resource.
A recurrence protocol
A classic scheme takes two noisy pairs, applies bilateral CNOT gates, measures the target pair, and keeps the source pair only when the measurements agree. Successful rounds concentrate fidelity; the process is repeated hierarchically. Hashing and breeding protocols instead act on large blocks and approach the optimal rate. All operate strictly within LOCC, since the parties cannot exchange quantum systems freely.
- Input: many low-fidelity entangled pairs
- Tools: local gates, local measurement, classical messages
- Output: fewer pairs with fidelity approaching one
- Cost: probabilistic discarding of failed rounds
Limits
Not all entanglement can be distilled. States with positive partial transpose are bound entangled and yield nothing. Even for distillable states the rate is bounded above by measures like the logarithmic negativity and relative entropy of entanglement. Distillation is generally irreversible: the pairs consumed to create a state can exceed those recoverable from it.
Why it matters
Distillation is the backbone of long-distance quantum communication. Entanglement sent through lossy fiber arrives degraded; distillation restores usable Bell pairs, which then power teleportation-based repeaters. It is equally central to fault tolerance, where noisy magic states are distilled into clean ones for non-Clifford gates. In both settings, distillation is how a noisy quantum channel is turned into a reliable resource.