Topological entanglement in a monitored Rashba nanowire ✛ ✦
Context
In condensed matter physics, topological phases are a revolution: they are protected by global symmetries and have no local order parameters. A key feature is the presence of edge modes, such as Majorana fermions in superconducting nanowires based on the proximity effect with an ordinary superconductor (BCS theory, John Bardeen). These modes promise error-resistant quantum computation. However, real systems always interact with the environment, and the question of how decoherence affects topological protection remains open. Disconnected entanglement entropy (DEE) — a recently proposed tool for detecting non-local topological entanglement — becomes a powerful probe here.
Methods
The researchers considered a Rashba nanowire model near an s-wave superconductor with a magnetic field. Its dynamics was described by the Lindblad equation with local spin-dependent particle loss operators. Underpinning this is the Schrödinger equation for a pure state, extended to a stochastic equation, and the superposition principle, allowing a pure state to be a coherent sum. Instead of averaging over all trajectories, they applied the quantum jump (unraveling) method, tracking the evolution of pure states along individual stochastic trajectories. Since the Hamiltonian is quadratic, the state remains Gaussian, which made it possible to compute correlation matrices and entropies for a large number of sites (up to 120) using numerical simulations. DEE was computed using the standard formula, where subsystems A and B are two disconnected blocks of the chain, in order to cancel area-law terms and isolate the topological contribution. The computation of entropy relies on the concept of quantum entanglement, first formulated by Erwin Schrödinger.
Results
The main result: regardless of whether the loss acts on the whole chain, only in the bulk, or only at the edges, the ensemble-averaged DEE remains at the level log 2 ≈ 0.693 for a long time. The characteristic time $t_c$, defined by the deviation of DEE from the topological value by more than 0.01, grows linearly with system size N (e.g., $t_c$ ≈ 5–10 in dimensionless units for N~100). This is confirmed for weak disorder in the chemical potential. Statistics of DEE changes under individual quantum jumps showed a sharp peak at zero: jumps do not instantly alter the non-local entanglement. Physically, unlike the SSH model where a jump at an edge immediately destroys the edge mode, here a quantum jump toggles the system between two degenerate topological ground states with different fermion parity, alternately creating and destroying a Majorana mode. This is a direct consequence of the Pauli exclusion principle for fermions and the absence of particle number conservation. However, each such jump also creates a finite energy — a parasitic quasiparticle near the edge. This quasiparticle moves ballistically at a speed on the order of the Fermi velocity and reaches the other boundary only after a time ~L/v. It is then that it introduces an additional entropy contribution, disrupting the delicate cancellation in DEE. Thus arises delayed poisoning, explaining the linear increase in the lifetime of topological entanglement. In the thermodynamic limit, DEE becomes eternal.
Implications
These results change the perception of the vulnerability of topological quantum correlations. It turns out that boundary dissipation is not necessarily fatal for topological protection if there is ground state degeneracy and no particle conservation law. This opens new perspectives for designing robust topological quantum devices, where monitoring could even be used to manipulate Majorana modes without immediate wave function collapse. The method also shows that DEE is a sensitive tool for distinguishing types of edge entanglement in open systems.
Future development
The topic may evolve towards studying the influence of different types of jumps (e.g., parity-preserving), as well as interactions and non-Markovian dynamics. It is important to understand whether the linear scaling holds for more realistic models of quasiparticle poisoning that account for Coulomb interaction. Another front is experimental realization: although DEE is hard to measure directly, recent advances in quantum tomography inspire hope.
Impact
The work will impact the development of topological quantum computers based on Majorana zero modes, as well as the general understanding of quantum phase transitions in non-equilibrium conditions and the physics of open quantum systems.
Next steps
Near-term steps include simulating larger systems to verify scaling and analyzing sensitivity to the dissipation profile, as well as experimental verification in hybrid semiconductor-superconductor nanowires.
Key open problems
This research is directly related to a major unsolved problem — creating stable topological qubits and understanding decoherence in multi-qubit systems. It also sheds light on the fundamental question of how quantum information spreads in open many-particle systems, including the paradox of how the classical world emerges from the quantum through measurements.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
This study examines the effect of decoherence on topological entanglement in a Rashba nanowire using the Lindblad equation and the quantum jump method. The authors compute the disconnected entanglement entropy (DEE) along stochastic trajectories and show that it retains its topological value of log 2 for a time that grows linearly with system size. They find that quantum jumps switch the system between degenerate topological states without immediately destroying nonlocal entanglement.
Where its strength is
The strength of this work lies in explicitly tracking the dynamics of DEE along individual quantum trajectories, which reveals the microscopic mechanism behind the resilience of topological entanglement to local losses. The linear growth of the DEE preservation time with system size provides a quantitative benchmark for estimating the lifetime of topological protection.
Where it could go next
- It might be interesting to compare the switching mechanism between topological states under quantum jumps with the hierarchy of temporal correlations in a qubit, where characteristic timescales of quantum information loss are also observed.based on: Death and Rebirth of Quantum Echo: A Hierarchy of Temporal Correlations in a Qubit arXiv:2505.01379v1
- Related work explores how noise can generate quantum order; a similar approach could be applied to more complex dissipative mechanisms, not just particle losses but also dephasing or pumping.based on: Noise Gives Birth to Quantum Order arXiv:2607.07801
- There is a study in the archive where topology retains memory of the initial state; one could apply memory analysis methods to DEE dynamics under various types of disorder.based on: Topology Holds Memory arXiv:2605.00770
Worth trying
- Test the DEE calculation in the presence of simultaneous losses and dephasing to verify the universality of the linear growth of protection time.
- Check whether the zero peak in the statistics of DEE changes persists under nonlocal quantum jumps, such as parity measurements.
- Investigate the effect of finite temperature on DEE using thermal states within the Gaussian formalism.
Why this may matter
Understanding how decoherence affects topological entanglement is critical for assessing the feasibility of topological quantum computation. The linear growth of protection time with system size suggests potential scalability, and the identified switching mechanism between topological states could inform the design of noise-resilient qubits based on Majorana modes.
Nearby works in our archive
- Death and Rebirth of Quantum Echo: A Hierarchy of Temporal Correlations in a Qubitsimilarity 0.64
- Superconductivity Without Heavy Atomssimilarity 0.63
- Noise Gives Birth to Quantum Ordersimilarity 0.63
- Topology Holds Memorysimilarity 0.63
- Quantum Shock: Why Edge Memory Doesn't Fadesimilarity 0.63
- Two Atoms Against Chaos: A Quantum Memory Recordsimilarity 0.62
The closest work in the archive sits at 0.64 by meaning — the usual level for our corpus.
Original abstract
as written by the authors arXiv:2606.25653
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.
Interestingly, the disconnected entanglement entropy equals log 2 regardless of the exact model, as long as it is in a topological phase — this is the quantum analog of the universal conductance in the quantum Hall effect.
This story echoes the idea from Peter Watts' novel 'Blindsight,' where consciousness is seen as a side effect of quantum processes: here monitoring creates the illusion of stable identity, while in reality the system is constantly being reborn.
Key numbers
- topological value of DEE: log 2 ≈ 0.693
- sizes of studied systems: N = 88, 96, 104, 112, 120
- loss rates: γ↑ = 1.0, γ↓ = 0.9 (in arbitrary units)
- characteristic time t_c for N=104 (uniform dissipation): ~5 (in inverse energy units)
- ballistic excitation propagation speed: ~1 (in units of lattice constant/time)