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arXiv:2408.00844 · Quantum

Improving entanglement purification through coherent superposition of roles

Jorge Miguel-Ramiro, Alexander Pirker, Wolfgang Dür

Published Apr 9, 2025• 7 citations
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Abstract

Entanglement purification and distillation protocols are essential for harnessing the full potential of quantum communication technologies. Multiple strategies have been proposed to approach and optimize such protocols, most however restricted to Clifford operations. In this paper, we introduce a superposed entanglement purification design strategy, leveraging coherent superpositions of the roles of entangled states to enhance purification efficiency, defining a new family of non-Clifford distillation protocols. We demonstrate how this approach can be hierarchically integrated with existing entanglement purification strategies, consistently improving protocols performance.

DOI
10.22331/q-2025-04-09-1702

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Entanglement purification and distillation protocols are essential for harnessing the full potential of quantum communication technologies. Multiple strategies have been proposed to approach and optimize such protocols, most however restricted to Clifford operations. In this paper, we introduce a superposed entanglement purification design strategy, leveraging coherent superpositions of the roles of entangled states to enhance purification efficiency, defining a new family of non-Clifford distillation protocols. We demonstrate how this approach can be hierarchically integrated with existing entanglement purification strategies, consistently improving protocols performance.
Entanglement purification protocols are fundamental primitives in quantum communication, enabling the distillation of high-quality entanglement using only local operations and classical communication. For large multipartite states, however, existing purification schemes typically require substantial resources and become progressively inefficient as system size increases. We introduce a new type of multipartite entanglement purification, Localized Entanglement Purification (LEP), a family of protocols that purify entanglement at the level of network regions rather than globally. By exploiting spatial noise asymmetries, LEP reduces resource consumption and enables scalable purification strategies for larger quantum systems.
High-fidelity entanglement shared between distant quantum systems is an essential resource for quantum communication and computation. Entanglement distillation addresses this need by converting multiple noisy Bell pairs into fewer higher-fidelity pairs, using only local quantum operations and classical communication. However, this approach typically requires a substantial overhead in the number of qubits. To bypass this hurdle, we propose to leverage the high-dimensional Hilbert space of a single pair of bosonic systems to store a large amount of entanglement, replacing the need for multi-qubit systems. To distill entanglement in such a setup, we devise a new entanglement distillation protocol, tailored for bosonic systems. The protocol converts a highly-entangled noisy state between two bosonic systems into a lower-dimensional but high-fidelity entangled state, using only local bosonic operations. We show that our protocol significantly enhances the fidelity of the entangled state in the presence of naturally occurring loss and dephasing errors. Compared to methods relying on multiple Bell pairs, our scheme offers a more hardware-efficient strategy, providing a practical route toward the realization of entanglement distillation.
Entanglement purification describes a primitive in quantum information processing, where several copies of noisy quantum states are distilled into a few copies of nearly pure states of high quality via local operations and classical communication. Especially in the multiparticle case, the task of entanglement purification is complicated, as many inequivalent forms of pure state entanglement exist and purification protocols need to be tailored for different target states. In this paper we present optimized protocols for the purification of hypergraph states, which form a family of multiqubit states that are relevant from several perspectives. We start by reformulating an existing purification protocol in a graphical language. This allows for systematical optimization and we present improvements in three directions. First, one can optimize the sequences of the protocol with respect to the ordering of the parties. Second, one can use adaptive schemes, where the measurement results obtained within the protocol are used to modify the protocols. Finally, one can improve the protocol with respect to the efficiency, requiring fewer copies of noisy states to reach a certain target state.
Generating quantum entanglement is plagued by decoherence. Distillation and error-correction are employed against such noise, but designing a good distillation circuit, especially on today’s imperfect hardware, is challenging. We develop a simulation algorithm for distillation circuits with per-gate complexity of O(1){\mathcal{O}}(1)O(1) , drastically faster than O(N){\mathcal{O}}(N)O(N) Clifford simulators or O(2N){\mathcal{O}}({2}^{N})O(2N) wavefunction simulators over N qubits. This simulator made it possible to optimize distillation circuits much larger than previously feasible. We design distillation circuits from n raw Bell pairs to k purified pairs and study the use of these circuits in the teleportation of logical qubits. The resulting purification circuits are the best-known for finite-size noisy hardware and can be fine-tuned for specific error-models. Furthermore, we design purification circuits that shape the correlations of errors in the purified pairs such that the performance of potential error-correcting codes is greatly improved.
In order to perform faithfully quantum communication protocols such as quantum teleportation, superdense coding, quantum key distribution, and quantum secret sharing, we need the entanglement purification process to make a maximal entanglement out of many copies of the partially entangled pairs by using local operations and classical communication. In this dissertation,\nwe analyze the efficiency of several entanglement purification protocols for qubit states and qudit states, and present a new efficient entanglement purification protocol. Furthermore, we show that our method can be applied to the existing best protocol\nso as to improve the efficiency.
Entanglement purification protocols (EPPs) are essential for quantum communication networks, which are the backbone of fault-tolerant, scalable distributed quantum information processing. While simplifying theoretical studies, the common assumption of identical input is almost never justified in reality. This dissertation investigates entanglement purification with non-identical input from three perspectives: what is fundamentally restricted, what is guaranteed, and how to enhance EPP performance. We first introduce the concept of input-independent universal EPPs and prove no-go theorems for their existence. Despite the no-go theorems, we prove guaranteed improvements that EPPs can achieve, with the 2-to-1 CNOT-based EPP as a canonical example. We also prove the optimal time to apply this EPP in realistic quantum repeater scenarios for typical error models and figures of merit. We then prove that shared randomness, a classical resource, can enhance the performance of an arbitrary nnn-to-1 bilocal Clifford entanglement purification protocol using the strategy of accumulating and shuffling in a multi-source scenario. Altogether, this dissertation offers insights into both the theoretical understanding of EPPs with non-identical input and the practical integration of EPPs into realistic quantum networks.