Guida and Colleagues Model Topological Entanglement Persistence for Robust Quantum States

Researchers at the University of Naples Federico II, led by Guida and colleagues from Scuola Superiore Meridionale, have demonstrated that the disconnected entanglement entropy (DEE), a crucial indicator of topological order, maintains its topological value for a period proportional to the system’s size. This persistence is observed even when dissipation, acting on the boundary, affects the topological Majorana modes within the system. The underlying mechanism enabling this phenomenon is the absence of particle conservation coupled with the degeneracy of the topological manifold. The research elucidates how continuous monitoring facilitates transitions between topological states, leading to the creation and annihilation of Majorana modes, and ultimately governing the decay of topological entanglement through the propagation of quasiparticles. Prolonged topological entanglement enabled by particle number dynamics in a superconducting nanowire Entanglement, a fundamental resource in quantum information processing, now persists for a time linear in system size, representing a significant advancement over previous limitations where stability diminished rapidly with increasing complexity. A monitored superconducting Rashba nanowire served as the experimental platform, extending a previously established approach originating from studies of the Su-Schrieffer-Heeger (SSH) chain. The Rashba nanowire, a one-dimensional system exhibiting strong spin-orbit coupling, supports the formation of Majorana modes at its boundaries under specific conditions. These Majorana modes are particularly interesting due to their non-Abelian statistics, making them potential building blocks for topologically protected quantum bits. The nanowire’s unique ability to gain or lose particles, a consequence of the monitoring process and the open nature of the system, allows for switching between topological states, transitioning between a topologically trivial phase and a topologically non-trivial phase. This process was previously unsustainable for extended durations due to the inherent fragility of quantum states. This behaviour arises from the degeneracy of the topological manifold, meaning multiple ground states possess the same energy and topological properties. This degeneracy enables transitions between these states via the creation and annihilation of Majorana modes, effectively delaying the decay of topological entanglement caused by propagating quasiparticles. Quasiparticles, representing excitations within the superconducting material, inevitably arise due to thermal fluctuations or imperfections in the system. The disconnected entanglement entropy (DEE), a measure of quantum connection between spatially separated parts of the system, specifically designed to isolate topological entanglement from contributions due to conventional entanglement, scales linearly with the nanowire’s size. Detailed analysis of the topological ground state revealed that the DEE is reliably quantized to approximately zero in the trivial phase, indicating the absence of topological order, and to log 2 in the topological phase, confirming its effectiveness as a robust indicator of the system’s topological state. The log 2 value is a direct consequence of the presence of a single pair of Majorana modes at the boundaries of the nanowire. Although quasiparticles, which carry entanglement, propagate ballistically, meaning they travel without scattering, their contributions to the overall entanglement entropy largely cancel each other out due to their opposing correlations, effectively preserving the topological signal. This cancellation is not complete, however, and ultimately leads to the decay of the DEE over time. Statistical analysis, performed on numerous quantum trajectories obtained through continuous monitoring, showed the DEE remains remarkably stable when quantum jumps, induced by the monitoring process, do not sharply disrupt the entanglement. Crucially, this stability correlates strongly with the nanowire’s length; longer nanowires exhibit prolonged topological stability. The monitoring process itself introduces a form of dissipation, but the careful design of the measurement scheme minimises its disruptive effects. Stable topological quantum states promise enhanced durability against environmental noise, a vital requirement for building practical and scalable quantum computers. Protecting quantum information from decoherence, the loss of quantum properties due to interaction with the environment, is one of the biggest challenges in quantum computing, and topological protection offers a promising solution. Guida and colleagues have now demonstrated that, despite unavoidable energy loss due to quasiparticle generation and the inherent dissipation associated with monitoring, a key measure of entanglement, the DEE, persists for a duration scaling with the size of a monitored superconducting nanowire. This finding is important as it demonstrates a surprising level of durability in topological entanglement, even in the presence of energy loss which inevitably degrades quantum states. The system readily switches between different quantum states, effectively creating and destroying Majorana modes, despite energy loss through quasiparticle propagation. This dynamic behaviour, facilitated by the monitoring process, allows for the exploration of the topological phase diagram and the characterisation of the Majorana modes. Topological entanglement, a potentially strong and robust form of quantum connection, endures in a realistically disturbed system, as clarified by this work. By meticulously tracking individual quantum events within a superconducting nanowire using a quantum-limited measurement scheme, the disconnected entanglement entropy remains topologically stable for a period scaling with the nanowire’s length, offering crucial insights into the mechanisms sustaining this stability and paving the way for the development of more robust quantum technologies. The observed linear scaling with system size suggests that increasing the length of the nanowire could further enhance the coherence time of the topological quantum state. The research demonstrated that a measure of quantum entanglement, the disconnected entanglement entropy, remained topologically stable for a duration proportional to the length of a monitored superconducting nanowire. This finding is important because it shows that topological entanglement can be surprisingly resilient to energy loss and environmental disturbance, both critical challenges in building quantum computers. The system dynamically switches between quantum states while maintaining this stability, facilitated by the monitoring process. The authors suggest that increasing the nanowire’s length may further extend the duration of this topological protection. 👉 More information 🗞 Long-lasting Topological Entanglement in a Monitored Rashba Nanowire ✍️ Emanuele Guida, Giulia Salatino, Gianluca Passarelli, Angelo Russomanno and Procolo Lucignano 🧠 ArXiv: https://arxiv.org/abs/2606.25653 Stay current. 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