Entanglement purification by counting and locating errors with entangling measurements

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