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arxiv: 2606.25653 · v1 · pith:NR75LEXUnew · submitted 2026-06-24 · 🪐 quant-ph · cond-mat.mes-hall

Long-lasting Topological Entanglement in a Monitored Rashba Nanowire

Emanuele Guida , Giulia Salatino , Gianluca Passarelli , Angelo Russomanno , Procolo Lucignano This is my paper

Pith reviewed 2026-06-25 21:09 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hall
keywords monitored quantum systemstopological entanglementRashba nanowireMajorana modesquantum trajectoriesdisconnected entanglement entropyopen quantum systemsquantum jumps
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The pith

The disconnected entanglement entropy in a monitored Rashba nanowire remains at its topological value for a time linear in system size.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines the topological properties of a Rashba chain subject to monitoring by following individual quantum-jump trajectories. It establishes that the disconnected entanglement entropy keeps its initial topological value for a duration that grows linearly with the length of the chain, even when the monitoring acts at the boundaries and perturbs the Majorana modes. The persistence occurs because particle number is not conserved and the topological sector is degenerate, so monitoring can flip the system between distinct topological configurations while it poisons finite-energy quasiparticles that would otherwise erase the entanglement. A reader would care because the result identifies a concrete mechanism that can keep topological entanglement alive longer under continuous observation than boundary dissipation alone would suggest.

Core claim

Along quantum-jump trajectories of a monitored Rashba nanowire, the disconnected entanglement entropy stays at its initial topological value for a time that scales linearly with system size. This holds even though dissipation occurs at the boundary and directly affects the topological Majorana modes. The underlying reason is the absence of particle conservation together with the degeneracy of the topological manifold: monitoring can switch the system between different topological states, alternately creating and annihilating a Majorana mode, while it simultaneously poisons finite-energy ballistically propagating quasiparticles that eventually destroy the topological entanglement structure.

What carries the argument

Disconnected entanglement entropy (DEE) evaluated along individual quantum-jump trajectories of the monitored Rashba chain, which tracks how topological character survives monitoring-induced switching and quasiparticle poisoning.

If this is right

  • The DEE remains topological for a time proportional to system size even under boundary monitoring.
  • Majorana modes can be created and annihilated by the monitoring process without immediate loss of topological entanglement.
  • Finite-energy quasiparticles are poisoned by the dynamics, postponing the destruction of the entanglement structure.
  • Switching between degenerate topological states is enabled by the lack of particle conservation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The linear scaling may set a practical upper limit on how long topological information can be protected in monitored open nanowires before quasiparticle poisoning wins.
  • Similar persistence might appear in other monitored topological chains if they also lack particle conservation and possess a degenerate ground-state manifold.
  • Varying the monitoring rate could shift the coefficient of the linear scaling and therefore change the usable lifetime of the topological entanglement.

Load-bearing premise

The absence of particle conservation and the degeneracy of the topological manifold allow monitoring to switch the system between different topological states while poisoning finite-energy quasiparticles.

What would settle it

Numerical or experimental measurement of the time at which the DEE first deviates from its topological value; that time should grow linearly with nanowire length if the central claim holds.

Figures

Figures reproduced from arXiv: 2606.25653 by Angelo Russomanno, Emanuele Guida, Gianluca Passarelli, Giulia Salatino, Procolo Lucignano.

Figure 1
Figure 1. Figure 1: Sketch of the partition used to compute the disconnected entanglement entropy. The green shaded region denotes subsystem A, while the yellow shaded regions denote subsystem B. Blue spheres represent Dirac fermions localized on the sites of the chain. designed to detect symmetry-protected topological phases, where the relevant non-local contribution is associated with boundary modes under open boundary cond… view at source ↗
Figure 2
Figure 2. Figure 2: DEE of the ground state of the isolated Rashba nanowire Hamiltonian as a function of the external magnetic field, for growing system sizes. 3vt. This contributions in Eq. (12) erase with each other leaving only the topological part. This cancellation starts to be disrupted after quasiparticles propagating from one cut have reached the nearest one, and the two cuts have started to affect each other so that … view at source ↗
Figure 3
Figure 3. Figure 3: (a) Occupation number ⟨niσ⟩ as a function of the site index i, in unitary regime and with N = 104. (b) Occupation number ⟨ni↑⟩ of the first twenty sites in the unitary regime, with N = 88, (c) N = 104, (d) N = 120. associated with the two Majorana edge modes. Its spatial density therefore provides a representative measure of the edge-state localization. In [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Plot of ρ1,↑ and ρ1,↓ versus site index i, with N = 104. (b) Spatial extension of ρ1,↑ for the first twenty sites. evolve the correlation matrix directly in time. The spectra of the reduced correlation matrices GX(t), X ∈ {A, B, A∩B, A∪B}, provide the corresponding trajectory-resolved entropies S traj(X), from which S D,traj is readily obtained. Averaging over an ensemble of Ntraj = 96 trajectories, we… view at source ↗
Figure 5
Figure 5. Figure 5: Evolution of the average DEE for a system prepared in the topological phase and subject to uniform dissipation. (a) W = 0, (b) W = 0.5, (c) W = 1.0. To quantify the duration of this plateau, we introduce a characteristic time interval [0, tc] over which the average DEE remains at the topological value. More precisely, following Refs. [26], we define tc = t traj c , where t traj c denotes, for a given traje… view at source ↗
Figure 6
Figure 6. Figure 6: displays the dependence of tc on the system size N for a system initially prepared in the quasiparticle vacuum of the topological phase and evolving under uniform dissipation. For weak disorder, the data remain compatible with a linear dependence on N; we therefore fit the data with a linear law, with the resulting fit parameters shown directly in the figure. The linear increase does not depend on the spec… view at source ↗
Figure 7
Figure 7. Figure 7: P(∆S D) obtained by evolving, for each trajectory, the system in the time interval [0, ttraj c ] and with N = 104 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Sketch of the Kitaev chain in the Majorana representation. Green dots denote Majorana degrees of freedom, while blue dots denote Dirac fermions localized on the physical sites of the chain. In the trivial phase, the ground state is naturally described in terms of Dirac fermions localized on each site. In the topological phase, instead, the relevant Dirac fermions are built from Majoranas belonging to neigh… view at source ↗
read the original abstract

We study the topological properties of a monitored Rashba chain along quantum-jump trajectories, investigating the persistence of the initial topological value of the disconnected entanglement entropy (DEE). We find that the DEE persists in its topological value for a time linear in the system size, even if the dissipation acts on the boundary and affects the topological Majorana modes. The reason for this phenomenon lies in the absence of particle conservation and in the degeneracy of the topological manifold, allowing the monitoring to let the system switch between different topological states -- alternatively creating and annihilating a Majorana mode -- while producing a poisoning of finite-energy ballistically propagating quasiparticles that eventually destroy the topological entanglement structure.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript studies the topological properties of a monitored Rashba chain along individual quantum-jump trajectories. The central claim is that the disconnected entanglement entropy (DEE) remains at its initial topological value for a time that scales linearly with system size, even when dissipation acts at the boundary and perturbs the Majorana modes. The proposed mechanism relies on the absence of particle-number conservation together with the degeneracy of the topological manifold, which permits the monitoring to switch the system between distinct topological sectors while finite-energy quasiparticles are poisoned and propagate ballistically, eventually destroying the entanglement after a time proportional to system length.

Significance. If the linear-in-size persistence is robustly demonstrated, the result would establish a concrete mechanism by which topological entanglement can survive monitoring-induced dissipation for parametrically long times in one-dimensional systems. This would be relevant to the broader study of measurement-induced phases and to proposals for topological protection in open quantum devices.

minor comments (2)
  1. The abstract states that the DEE 'persists in its topological value for a time linear in the system size,' but the manuscript should explicitly define the precise quantity used for the DEE (e.g., which bipartition and which reference state) already in the introduction or methods section.
  2. Figure captions and axis labels should state the system sizes, monitoring rates, and disorder realizations over which the linear scaling is averaged; without this information the reader cannot assess the statistical significance of the reported time scale.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, accurate summary of the central claim, and recommendation for minor revision. No specific major comments were listed under the MAJOR COMMENTS section of the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper presents a physical mechanism for long-lasting topological DEE under monitoring, attributing persistence to lack of particle conservation and degeneracy allowing state switching while poisoning quasiparticles. No equations, fitted parameters, self-citations, or ansatzes appear in the provided text that reduce any claim to its own inputs by construction. The argument is self-contained as an explanatory model consistent with standard monitored quantum dynamics and topology, with no load-bearing steps that qualify under the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the central claim rests on unstated model assumptions about the Rashba Hamiltonian and monitoring protocol.

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