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arXiv:2106.09240 · Physical Review Research

Robust multipartite entanglement without entanglement breaking

Ming‐Xing Luo, Shao-Ming Fei

Published Nov 16, 2021• 16 citations
arXivHTMLPDF

Abstract

Entangled systems in experiments may be lost or off-line in distributed quantum information processing. This inspires a general problem to characterize quantum operations, which result in breaking of entanglement or not. Our goal in this paper is to solve this problem both in single entanglement and network scenarios. We firstly propose a local model for characterizing all entangled states that are breaking for losing particles. This implies a simple criterion for witnessing single entanglement such as generalized GHZ states and Dicke states. It further provides an efficient witness for entangled quantum networks depending on its connectivity such as $k$-independent quantum networks, completely connected quantum networks, and $k$-connected quantum networks. These networks are universal resources for measurement-based quantum computations. The strong nonlocality can be finally verified by using nonlinear inequalities. These results show distinctive features of both single entangled systems and entangled quantum networks.

DOI
10.1103/physrevresearch.3.043120

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The multipartite correlations derived from local measurements on some composite quantum systems are inconsistent with those reproduced classically. This inconsistency is known as the quantum nonlocality and shows a milestone in the foundations of quantum theory. Still, it is NP hard to decide a nonlocal quantum state. We investigate an extended question as to how to characterize the nonlocal properties of quantum states that are distributed and measured in networks. We first prove the generic tripartite nonlocality of chain-shaped quantum networks using semiquantum nonlocal games. We then introduce an approach to prove the generic activated nonlocality as a result of entanglement swapping for all the bipartite entangled states. The result is further applied to show the multipartite nonlocality and activated nonlocality for all the nontrivial quantum networks consisting of any entangled states. Our results provide the nonlocality witnesses and quantum superiorities of all the connected quantum networks or nontrivial hybrid networks in contrast to classical networks.
Entangled quantum networks provide great flexibilities and scalabilities for quantum information processing or quantum Internet. Most of results are focused on the nonlocalities of quantum networks. Our goal in this work is to explore new characterizations of any networks with theory-independent configurations. We firstly prove the configuration inequality for any network using the fractional independent set of the associated graph. These inequalities can be built with polynomial-time complexity. The new result allows featuring correlations of any classical network depending only on its network topology. Similar inequalities hold for all entangled quantum networks with any local measurements. This shows an inherent feature of quantum networks under local unitary operations. It is then applied for verifying almost all multipartite entangled pure states with linear complexity, and witnessing quantum network topology without assumption of inputs. The configuration theory is further extended for any no-signalling networks. These results may be interesting in entanglement theory, quantum information processing, and quantum networks.
The quantum entanglement as one of very important resources has been widely used in quantum information processing. In this work, we present a new kind of genuine multipartite entanglement. It is derived from special geometric feature of entangled systems compared with quantum multisource networks. We prove that any symmetric entangled pure state shows stronger nonlocality than the genuinely multipartite nonlocality in the biseparable model. Similar results hold for other entangled pure states with local dimensions no larger than 333. We further provide computational conditions for witnessing the new nonlocality of noisy states. These results suggest that the present model is useful characterizing a new kind of generic quantum entanglement.
Abstract Bell inequalities have long been essential for the device-independent detection of entanglement. This study introduces subcorrelation Bell inequalities as a robust framework for detecting entanglement and probing quantum non-locality. We derived a family of such inequalities, categorized according to their dependence on measurement settings, and numerically identified 19 distinct quantum states that achieve the maximal violation of these inequalities. Importantly, our focus on maximal violation is not for its own sake but because, in this framework, maximal violation directly corresponds to maximal robustness of nonlocal correlations against particle loss. This connection reveals a broad class of multipartite entangled states that remain resilient under loss, making them highly relevant for practical implementations of quantum information protocols. We further characterized their entanglement properties using concurrence and the geometric measure, confirming their utility for critical areas such as quantum communication, cryptography, and device-independent protocols. The framework established herein sets the stage for future investigations, including the generalization of these inequalities to higher-dimensional systems and a more comprehensive characterization of their robustness against various forms of noise, thereby expanding the potential for non-local states to drive progress in quantum technologies.