Single-copy entanglement purification: a robust approach for diverse noise sources

Effectively managing various types of decoherence is crucial for leveraging entanglement in quantum information processing and quantum computing. In this paper, we propose purification circuits that deterministically produce a maximally entangled state from a single copy of an imperfect entangled pair affected by various noise sources. Unlike conventional methods, our approach eliminates the need for multiple copies of the entangled state, pre-purification operations, and imposes no restrictions on the initial entanglement fidelity of the imperfect pair. Our method utilizes ancilla qubits and CNOT gates to address errors from Pauli X and Z (bit flip and phase flip), as well as combinations of these errors that create general mixed entangled states and amplitude-damped entangled states. Our analysis shows that noisy CNOT gates impact fidelity minimally, with only the final two gates being critical. We validate our approach through mathematical analysis and practical implementation in Qiskit, demonstrating its effectiveness and robustness.