Universal and Optimal Error Thresholds for Measurement-Based Entanglement Purification

We investigate measurement-based entanglement purification protocols (EPP) in the presence of local noise and imperfections. We derive a universal, protocol-independent threshold for the required quality of the local resource states, where we show that local noise per particle of up to 24% is tolerable. This corresponds to an increase of the noise threshold by almost an order of magnitude, based on the joint measurement-based implementation of sequential rounds of few-particle EPP. We generalize our results to multipartite EPP, where we encounter similarly high error thresholds.

Figure 1

Resource states (red, outer columns) up to local unitary operations for one (top) and two (bottom) purification steps using the protocol of Deutsch et al. We use standard graph state notation. The Bell pairs (yellow, inner columns) are coupled to the resource states via Bell measurements.

Figure 2

Illustration of concatenation of resource states for two purification steps. The dashed boxes indicate Bell measurements.