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Localizing multipartite entanglement with local and global measurements

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Researchers introduced two new measures—multipartite entanglement of assistance (MEA) and localizable multipartite entanglement (LME)—to quantify how entanglement can be concentrated onto subsystems via measurements, extending prior bipartite frameworks. The team derived computable bounds and proved Lipschitz-continuity for these measures using n-tangle, genuine multipartite concurrence, and concentratable entanglement, enabling practical analysis of entanglement localization in experiments. A matrix-based criterion was developed to determine whether specific graph states can be transformed into target states with desired n-tangle values, offering no-go theorems beyond standard local Clifford operations. The framework validates the near-optimality of local protocols converting line graph states into GHZ states, even compared to arbitrary entangled measurements, addressing a key challenge in measurement-based quantum computation. MEA and LME were also shown to detect phase transitions in transverse-field Ising models, highlighting their broader utility in quantum networking and critical phenomena studies.

Localizing multipartite entanglement with local and global measurements

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AbstractWe study the task of localizing multipartite entanglement in pure quantum states onto a subsystem by measuring the remaining systems. To this end, we fix a multipartite entanglement measure and consider two quantities: the multipartite entanglement of assistance (MEA), defined as the entanglement measure averaged over the post-measurement states and maximized over arbitrary measurements; and the localizable multipartite entanglement (LME), defined in the same way but restricted to only local single-system measurements. Both quantities generalize previously considered bipartite entanglement localization measures. In our work we choose the n-tangle, the genuine multipartite entanglement concurrence and the concentratable entanglement (CE) as the underlying seed measure, and discuss the resulting MEA and LME quantities. First, we prove easily computable upper and lower bounds on MEA and LME and establish Lipschitz-continuity for the n-tangle and CE-based LME and MEA. Using these bounds we investigate the typical behavior of entanglement localization by deriving concentration inequalities for the MEA evaluated on Haar-random states and performing numerical studies for small tractable system sizes. We then turn our attention to protocols that transform graph states. We give a simple criterion based on a matrix equation to decided whether states with a specified n-tangle value can be obtained from a given graph state, providing no-go theorems for a broad class of such graph state transformations beyond the usual “local Clifford plus local Pauli measurement” framework. This analysis is generalized to weighted graph states, which provide a realistic error model in current experiments preparing graph state. Our entanglement localization framework certifies the near-optimality of recently discussed local-measurement protocols to transform uniformly weighted line graph states into GHZ states, even when considering arbitrary entangled measurements. Finally, we demonstrate how our MEA and LME quantities can be used to detect critical phenomena such as phase transitions in transversal field Ising models. Since entanglement localization is operationally relevant throughout quantum networking and measurement-based quantum computation, our framework of results based on the MEA and LME has the potential for broad applications in these fields.Popular summaryQuantum entanglement is a unique form of correlation between physical systems without an analogue in classical physics. Numerous protocols in quantum information science require entanglement as a critical resource. Thus, a reliable method of producing highly entangled states on quantum systems comprised of many particles is desirable. One way of doing this is taking a larger, possibly less entangled system containing additional particles, performing a quantum measurement on the additional particles, and then discarding them, with the goal of localizing entanglement on the remaining systems. This approach has been the focus of a number of recent proposals for preparing quantum states. In this work, we introduce a framework for analyzing and benchmarking such protocols. The basic tool of this framework is a variant of a quantity known as localizable entanglement (LE), which describes the maximum amount of multipartite entanglement that one can generate on average by performing measurements on additional systems. To enable the practical use of the LE, we derive a set of bounds on the LE that are easy to compute and may be probed by experiments. These bounds enable us to make broad conclusions about measurement-based protocols for generating entanglement in a diverse set of scenarios. As an example, our bounds yield a criterion that efficiently deduces what sort of graph states – an important family of multipartite quantum states – may be prepared from other graph states in many cases, a problem that is notoriously computationally difficult. We anticipate that this criterion may be useful in identifying ideal states for entanglement-generating protocols.► BibTeX data@article{Vairogs2026localizing, doi = {10.22331/q-2026-02-23-2007}, url = {https://doi.org/10.22331/q-2026-02-23-2007}, title = {Localizing multipartite entanglement with local and global measurements}, author = {Vairogs, Christopher and Hermes, Samihr and Leditzky, Felix}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2007}, month = feb, year = {2026} }► References [1] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters. ``Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels''.

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Could not fetch ADS cited-by data during last attempt 2026-02-23 12:59:32: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe study the task of localizing multipartite entanglement in pure quantum states onto a subsystem by measuring the remaining systems. To this end, we fix a multipartite entanglement measure and consider two quantities: the multipartite entanglement of assistance (MEA), defined as the entanglement measure averaged over the post-measurement states and maximized over arbitrary measurements; and the localizable multipartite entanglement (LME), defined in the same way but restricted to only local single-system measurements. Both quantities generalize previously considered bipartite entanglement localization measures. In our work we choose the n-tangle, the genuine multipartite entanglement concurrence and the concentratable entanglement (CE) as the underlying seed measure, and discuss the resulting MEA and LME quantities. First, we prove easily computable upper and lower bounds on MEA and LME and establish Lipschitz-continuity for the n-tangle and CE-based LME and MEA. Using these bounds we investigate the typical behavior of entanglement localization by deriving concentration inequalities for the MEA evaluated on Haar-random states and performing numerical studies for small tractable system sizes. We then turn our attention to protocols that transform graph states. We give a simple criterion based on a matrix equation to decided whether states with a specified n-tangle value can be obtained from a given graph state, providing no-go theorems for a broad class of such graph state transformations beyond the usual “local Clifford plus local Pauli measurement” framework. This analysis is generalized to weighted graph states, which provide a realistic error model in current experiments preparing graph state. Our entanglement localization framework certifies the near-optimality of recently discussed local-measurement protocols to transform uniformly weighted line graph states into GHZ states, even when considering arbitrary entangled measurements. Finally, we demonstrate how our MEA and LME quantities can be used to detect critical phenomena such as phase transitions in transversal field Ising models. Since entanglement localization is operationally relevant throughout quantum networking and measurement-based quantum computation, our framework of results based on the MEA and LME has the potential for broad applications in these fields.Popular summaryQuantum entanglement is a unique form of correlation between physical systems without an analogue in classical physics. Numerous protocols in quantum information science require entanglement as a critical resource. Thus, a reliable method of producing highly entangled states on quantum systems comprised of many particles is desirable. One way of doing this is taking a larger, possibly less entangled system containing additional particles, performing a quantum measurement on the additional particles, and then discarding them, with the goal of localizing entanglement on the remaining systems. This approach has been the focus of a number of recent proposals for preparing quantum states. In this work, we introduce a framework for analyzing and benchmarking such protocols. The basic tool of this framework is a variant of a quantity known as localizable entanglement (LE), which describes the maximum amount of multipartite entanglement that one can generate on average by performing measurements on additional systems. To enable the practical use of the LE, we derive a set of bounds on the LE that are easy to compute and may be probed by experiments. These bounds enable us to make broad conclusions about measurement-based protocols for generating entanglement in a diverse set of scenarios. As an example, our bounds yield a criterion that efficiently deduces what sort of graph states – an important family of multipartite quantum states – may be prepared from other graph states in many cases, a problem that is notoriously computationally difficult. We anticipate that this criterion may be useful in identifying ideal states for entanglement-generating protocols.► BibTeX data@article{Vairogs2026localizing, doi = {10.22331/q-2026-02-23-2007}, url = {https://doi.org/10.22331/q-2026-02-23-2007}, title = {Localizing multipartite entanglement with local and global measurements}, author = {Vairogs, Christopher and Hermes, Samihr and Leditzky, Felix}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2007}, month = feb, year = {2026} }► References [1] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. Wootters. ``Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels''.

Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-49208-9 [20] Robert Raussendorf and Hans J. Briegel. ``A one-way quantum computer''.

Physical Review Letters 78, 5022–5025 (1997). https://doi.org/10.1103/PhysRevLett.78.5022 [78] Mark M. Wilde. ``Quantum information theory''.

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