SciPost Submission Page
Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces
by Hai-Long Shi, Augusto Smerzi, Luca Pezzè
Submission summary
| Authors (as registered SciPost users): | Hailong Shi |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202501_00002v1 (pdf) |
| Date submitted: | 2025-01-05 01:22 |
| Submitted by: | Shi, Hailong |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Multipartite entanglement is a crucial resource for advancing quantum technologies, with considerable research efforts directed toward achieving its rapid and scalable generation. In this work, we derive an analytical expression for the time-averaged quantum Fisher information (QFI), enabling the detection of scalable multipartite entanglement dynamically generated by all quantum chaotic systems governed by Dyson's ensembles. Our approach integrates concepts of randomness and quantum chaos, demonstrating that the QFI is universally determined by the structure and dimension of the Krylov space that confines the chaotic dynamics. In particular, the QFI ranges from $N^2/3$ for $N$ qubits in the permutation-symmetric subspace (e.g. for chaotic kicked top models with long-range interactions), to $N$ when the dynamics extend over the full Hilbert space with or without bit reversal symmetry or parity symmetry (e.g. in chaotic models with short-range Ising-like interactions). In the former case, the QFI reveals multipartite entanglement among $N/3$ qubits and highlights the power of chaotic collective spin systems in generating scalable multipartite entanglement. Interestingly this result can be related to isotropic substructures in the Wigner distribution of chaotic states and demonstrates the efficacy of quantum chaos for Heisenberg-scaling quantum metrology. Finally, our general expression for the QFI agrees with that obtained for random states and, differently from out-of-time-order-correlators, it can also distinguish chaotic from integrable unstable spin dynamics.
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
Current status:
Reports on this Submission
Strengths
- Very clear presentation.
- Clear result.
- New knowledge on use of various chaos indicators.
- Possible relevance for experiments.
Weaknesses
The various chaos measures could be differentiated better.
Report
The message of this paper is very clear and the presentation is excellent. I suggest publication in this open access journal after some minor suggestions have been addressed which I list in the following:
1) very few formal problems should be solved, e.g. ref. 88 is already cited as ref. 71, and Fig. 2 I suggest to divide into two subplots for better readability.
2) what I learn from this paper is that OTOCS do predict the correct short-term evolution (LE etc.) but may not be the best indicator for long-term mixing. This asymptotic statement might be differentiated a bit better together with other possible differences between the various chaos measures.
Requested changes
See report 1)-2).
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
1. Extend the observation, that random states may have large QFI from [38] to a chaotic evolution case.
2. One of the main results Eq. (2) is very general, applicable for the broad class of models.
3. The general theorem is nicely supported with analysis of the examples with useful numerical plots (easily readable and didactic).
Weaknesses
1. Unclear relation to the references [26-28].
2. Unreliable discussion on application in quantum metrology in Conclusion.
Report
The report is attached as a pdf file.
Requested changes
The requested changes are listed in the report pdf file.
Recommendation
Ask for minor revision