SciPost Submission Page
The Fate of Entanglement
by Gilles Parez, William Witczak-Krempa
Submission summary
| Authors (as registered SciPost users): | Gilles Parez |
| Submission information | |
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| Preprint Link: | scipost_202505_00056v2 (pdf) |
| Date accepted: | Dec. 2, 2025 |
| Date submitted: | Nov. 11, 2025, 9:36 p.m. |
| Submitted by: | Gilles Parez |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Quantum entanglement manifests itself in non-local correlations between the constituents of a system. In its simplest realization, a measurement on one subsystem is affected by a prior measurement on its partner, irrespective of their separation. For multiple parties, purely collective types of entanglement exist but their detection, even theoretically, remains an outstanding open question. Here, we argue that all forms of multipartite entanglement entirely disappear during the typical evolution of a physical state as it heats up, evolves in time in a large family of dynamical protocols, or as its parts become separated. We focus on the generic case where the system interacts with an environment. These results mainly follow from the geometry of the entanglement-free continent in the space of physical states, and hold in great generality. We illustrate these phenomena with a frustrated molecular quantum magnet in and out of equilibrium, and a quantum spin chain. In contrast, if the particles are fermions, such as electrons, another notion of entanglement exists that protects bipartite quantum correlations. However, genuinely collective fermionic entanglement disappears during typical evolution, thus sharing the same fate as in bosonic systems. These findings provide fundamental knowledge about the structure of entanglement in quantum matter and architectures, paving the way for its manipulation.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
Dear Referee,
We thank you for your report and valuable comments, which we address below.
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We agree that our results, as formulated, apply to subsystems of finite Hilbert space dimension, even when the total system is infinite in the thermodynamic limit. We have added a clarifying sentence at the end of the paragraph below Eq. (1) to make this explicit.
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It is indeed true that quenches of finite closed quantum systems will show revivals. However, this will typically occur at such large times that it is not very relevant. In practice, small subregions (compared to the complement) effectively thermalize, and the loss of entanglement holds for very long periods of time unless there is some fine-tuning in the quench. For instance, in the Icosahedral Ising model, we have not seen any revivals up to times of order $10^3$ (in units of 1/J).
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A discussion of possible counterexamples is indeed valuable. In Sec. II.C we have clarified that our general discussion pertains to global quenches, and we have added a short discussion at the end of the first paragraph of the section addressing the case of local quenches. Whether local quenches can indeed evade the fate of entanglement discussed here remains an open question for future work. Concerning topological order and many-body scars, we have added a corresponding remark in the conclusion.
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The question of how the fate of entanglement behaves with increasing number of spins is indeed a very important one. As correctly pointed out, the island of separability shrinks for larger $m$, implying that $m$-partite entanglement becomes more robust as $m$ increases. For instance, in Fig. 2(c), the critical temperature for 3-spin separability is higher than that for 2-spin separability, and the same holds for the characteristic times in Fig. 2(d). Our approach in this paper is to establish general and robust statements for $m$-partite separability at fixed $m$, and then illustrate them with examples. We have not analyzed in detail the scaling of the critical parameters—e.g. temperature $T_m^*$ or time $t_m^*$—with $m$. While this is indeed an important question deserving future investigation, it lies beyond the present scope of our paper. Second, if we fix the number of parties $m$, but increase the number of qubits within each party $n$ by making the subregion larger, it is an important question to understand how the results scale with increasing $n$.
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The papers you mention are interesting. In particular the methods mentioned in the PRL could lead to efficiently getting the RDM of a small subregion as a function of time, which would allow one to study its Fate of Entanglement. We have added a comment and a reference at the end of Sec. V.B.
Sincerely,
The authors
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)