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How does the entanglement entropy of a many-body quantum system change after a single measurement?
by Bo Fan, Can Yin, Antonio M. García-García
Submission summary
| Authors (as registered SciPost users): | Bo Fan · Antonio Miguel García García |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2504.04071v2 (pdf) |
| Date submitted: | May 4, 2025, 9:39 a.m. |
| Submitted by: | García García, Antonio Miguel |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
For one-dimensional free Dirac fermions, we compute numerically the probability distribution of the change in the entanglement entropy (EE), after the saturation time, resulting from a single measurement of the occupation number by using different measurement protocols. For the quantum jump and the projective measurement protocols, we observe clear deviations from Gaussianity characterized by broader and asymmetric tails, exponential for positive values of the change, and a peak at zero that increases with the system size and the monitoring strength supporting that in all cases the EE is in the area law phase. Another distinct feature of the distribution is its spatial inhomogeneity. In the weak monitoring limit, the distribution is close to Gaussian with a broad support for boundary point separating the two subsystems defining the EE while for the rest of sites has asymmetric exponential tails and a much narrower support. For a quantum state diffusion protocol, the distribution is Gaussian for weak monitoring. As the monitoring strength increases, it gradually develops symmetric exponential tails. In the strong monitoring limit, the tails are still exponential but the core turns from Gaussian to strongly peaked at zero suggesting the dominance of quantum Zeno effect. For all monitoring strengths, the distribution is size independent.
Author indications on fulfilling journal expectations
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report
This manuscript is about the monitored quantum dynamics of one-dimensional complex free fermions. The authors numerically studied three protocols of continuous monitoring (of the local occupation number): quantum state diffusion (QSD), quantum jumps (QJ), and local projective measurements (PM). They focused on the distribution of the bipartite entanglement entropy change due to a single measurement (during a short time in the case of QSD).
In general, the distribution is observed to be non Gaussian, except in the weak monitoring strength limit of QSD. The non-Gaussian distributions have a sharp peak at zero and broad tails, especially in the strong monitoring regime. This can be understood by considering the position of the measurements: most of them happen far away from the bipartition boundaries, and have little effect on the entanglement entropy.
The paper is clearly written. The results are quite reasonable and a useful addition to the literature. However the significance seems unclear. The implication for the phase diagram of this model is quite speculative and inconclusive. The results are characterised and discussed in a qualitative way. The fits to numerical data have little theoretical motivation.
Therefore I would rather recommend the paper to SciPost Core.
Questions that the authors may consider: - In figure 4 and 13, can one try to collapse the tails, for example by multiplying $P(\Delta S)$ by the system size $L$? - In figure 7 and 15, does the marginal distribution of $n_i$ change smoothly as a function of $\gamma$?
Recommendation
Accept in alternative Journal (see Report)