Quantum multipartite entanglement : classification and use for quantum information

Marcus Huber, Nicolai Friis, A. Gabriel +2 more

We analyze multipartite entanglement in systems of spin-½ particles from a relativistic perspective. General conditions which have to be met for any classification of multipartite entanglement to be Lorentz invariant are derived, which contributes to a physical understanding of entanglement classification. We show that quantum information in a relativistic setting requires the partition of the Hilbert space into particles to be taken seriously. Furthermore, we study exemplary cases and show how the spin and momentum entanglement transforms relativistically in a multipartite setting.

Roman Gielerak

Shuo Cheng, Junli Li, Cong‐Feng Qiao

We develop a novel method in classifying the multipartite entanglement state of 2×N ×N under stochastic local operations and classical communication (SLOCC). In this method, all inequivalent classes of a genuine entangled state can be assorted directly without knowing the classification information of lower dimension ones for any given dimension N. It also gives a nature explanation for the non-local parameters remaining in the entanglement classes when N ≥ 4. Entanglement is at the heart of the quantum information theory (QIT) and is now thought as a physical resource to realize quantum information tasks, such as quantum cryptography [1, 2], superdense coding [3, 4], and quantum computation [5]. The study of entanglement improves our further understanding of quantum non-locality [6] and also is of particular interest in QIT. One such case is the classification of multipartite entanglement. Two quantum states can be employed to implement the same tasks in QIT and are thought to be equivalent while they are mutually convertible by Stochastic Local Operations and Classical Communication (SLOCC) [7]. Nevertheless, in practice the classification of multipartite entanglement and in high dimensions in the Hilbert space seems to be a formidable task [8]. Matrix decomposition keeps to be a useful tool as in the two-partite case [9, 10]. A widely adopted philosophy in dealing with this issue is first to know the classification of the state in lower dimension (or less partite) and then extend to the higher dimension case [11, 12] (or more partite [13, 14]) in an inductive way. However, nontrivial aspect emerges as the dimension increases, i.e. some non-local parameters may nest in the entangled states [15, 16]. In literature, in

Dariusz Chruściński

Wei Cui

Entanglement is one of the fundamental features of quantum information science. Though bipartite entanglement has been analyzed thoroughly in theory and shown to be an important resource in quantum computation and communication protocols, the theory of entanglement shared between more than two parties, which is called multipartite entanglement, is still not complete. This book contains Dr. Wei Cui's research regarding the classification of multipartite entanglement and the transformation property between different multipartite states by local operators and classical communications (LOCC), which are two fundamental questions in the theory of multipartite entanglement.

Qiyi Li, Xiao Zheng, Guofeng Zhang

Quantum entanglement is a crucial resource in quantum information processing, yet its efficient, scalable and robust classification in multipartite systems remains theoretically challenging. Although supervised machinelearning has been applied to this task, most existing methods still suffer from high measurement costs, computational consumption, and weak noise robustness. In this work, by incorporating multipartite uncertainty relations as prior guidance, we propose a neural network approach to classify distinct Stochastic Local Operations and Classical Communication (SLOCC) multipartite entanglement classes based on states sampled from their local unitary (LU) orbits. Compared with traditional techniques, our method reduces experimental measurement-resource requirements and computational overhead, showing high adaptability to large-scale systems. The classification accuracy of our method reaches 99.5% in 20-qubit systems. The numerical validation is performed on states generated by random LU transformations, which preserve the SLOCC class. Within this setting, the proposed method offers strong effectiveness, scalability, and robustness for multipartite entanglement classification.