Local manipulation of multipartite entanglement

Jungmin Lee, Sung Dahm Oh

Lin-Mei Liang, Ping‐Xing Chen, Cheng-Zu Li +1 more

Rafael Chaves, Leandro Aolita, Antonio Acín

One of the main challenges for the manipulation and storage of multipartite entanglement is its fragility under noise. We present a simple recipe for the systematic enhancement of the resistance of multipartite entanglement against any local noise with a privileged direction in the Bloch sphere. For the case of exact local dephasing along any given basis, and for all noise strengths, our prescription grants full robustness: Even states with exponentially decaying entanglement are mapped to states whose entanglement is constant. In contrast to previous techniques resorting to complex logical-qubit encodings, such enhancement is attained simply by performing local-unitary rotations before the noise acts. The scheme is therefore highly experimentally friendly, as it brings no overhead of extra physical qubits to encode logical ones. In addition, we show that, apart from entanglement, the resiliences of the relative entropy of quantumness and the usefulness as resources for practical tasks such as metrology and nonlocality-based protocols are equivalently enhanced.

Shashank Shekhar, David Elkouss, Siddhartha Santra

Long-range, genuine multipartite entanglement (GME) between distant parties in a quantum network is a crucial resource for distributed quantum information processing. Through controlled manipulation of short-range GME states in the network via stochastic local operations aided by classical communication (SLOCC), long-range GME can be established between selected target nodes on demand. Optimizing such multipartite entanglement distribution protocols under constraints imposed by the network architecture, target-node set, and available resource budget is a key challenge in resource-efficient manipulation of GME. We present a general operational framework for manipulating GME in quantum networks by classifying the relevant networking operations into three broad primitives-inflation, deflation, and purification-reflecting their effect on the proliferation of GME through general bounds and illustrative examples. We show how these primitives can be combined to construct a broad class of multipartite quantum repeater protocols, enabling their systematic optimization, and demonstrate the framework with a simple example. Applying our approach to networks of Dür-Cirac-Tarrach states reveals a rich landscape of achievable end-to-end GME and accessible entanglement classes. More generally, our framework provides a systematic approach to the construction and optimization of multipartite quantum repeater protocols for scalable and resource-efficient GME distribution in quantum networks.

Ghofrane Bel-Hadj-Aissa

Yu Tian, Yuefei Liu, Xiangyi Meng

Multipartite entanglement, linking multiple nodes simultaneously, is a higher-order correlation that offers advantages over pairwise connections in quantum networks (QNs). Creating reliable, large-scale multipartite entanglement requires entanglement routing, a process that combines local, short-distance connections into a long-distance connection, which can be considered as a transformation of network topology. Here, we address the question of whether a QN can be topologically transformed into another via entanglement routing. Our key result is an exact mapping from multipartite entanglement routing to Nash-Williams's graph immersion problem, extended to hypergraphs. This generalized hypergraph immersion problem introduces a partial order between QN topologies, permitting certain topological transformations while precluding others, offering discerning insights into the design and manipulation of higher-order network topologies in QNs.