Entanglement purification by counting and locating errors with entangling measurements

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.

(see also "Entanglement-assisted entanglement purification" for a short version summarizing the main results.)

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• Experimental one-step deterministic entanglement purification
• Entanglement-assisted entanglement purification
• Quantum Repeater for W states
• Enumerating all bilocal Clifford distillation protocols through symmetry reduction
• Thresholds for the distributed surface code in the presence of memory decoherence
• Near-term $n$ to $k$ distillation protocols using graph codes
• Stabilizer Entanglement Distillation and Efficient Fault-Tolerant Encoders
• Collective Operations Can Exponentially Enhance Quantum State Verification
• Improving entanglement purification through coherent superposition of roles
• A modular entanglement-based quantum computer architecture
• Nondestructive Verification of Entangled States via Fidelity Witnessing
• Performance of entanglement purification including maximally entangled mixed states