Entanglement purification by counting and locating errors with entangling measurements

TL;DR

This paper introduces entanglement purification protocols that utilize high-dimensional auxiliary entangled systems to identify and correct errors in multiple qubit copies, improving fidelity especially when few errors are present.

Contribution

It presents a novel method using high-dimensional entangled auxiliary states and counter gates to efficiently purify multiple qubit copies, bridging the gap between small-scale and large-scale protocols.

Findings

Higher achievable fidelity compared to standard protocols

Effective for states with few initial errors

Generalizes to multi-party GHZ states

Abstract

We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about number and positions of errors in the noisy ensemble in an explicit and controlled way, thereby reducing the amount of noise in the ensemble and purifying the remaining states. This allows us to design entanglement purification protocols for any number of copies that work particularly well for a small number of expected errors, i.e. high fidelity of initial states. The main tool is a counter gate with which the required non-local information can be transferred into the high-dimensional entangled qudit auxiliary states. We compare our schemes to standard recurrence protocols that operate on pairs of copies, and hashing and breeding protocols that operate on a (asymptotically) large number of copies. Our protocols interpolate between these two regimes, leading to a higher achievable fidelity and yield. We illustrate our approach for bipartite qubit states, and generalize it to purify multi-party GHZ states.