Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons

In the article titled “Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons” published in 2022, the authors investigate the fascinating behavior of quantum states in many-particle systems exhibiting anyonic exchange statistics in one spatial dimension. Anyons are particles that interpolate between bosons and fermions, and this study treats the exchange statistics parameter ( \kappa ) as a continuously tunable variable rather than a fixed discrete label. This approach effectively recasts the anyon-anyon mapping as a smooth transformation, which allows the authors to explore the geometry of quantum states as a function of ( \kappa ). Key to their analysis is the finding that while bosonic and fermionic states remain orthogonal (completely distinct), overlaps between anyonic states with differing ( \kappa ) are nonzero and decay according to a universal orthogonality catastrophe. This phenomenon is governed by a fundamental statistical factor independent of the specific microscopic Hamiltonian, indicating a deeply rooted structural property of these quantum systems. The decay of overlap with changing statistics ties to quantum speed limits, which provide constraints on how fast these quantum states can evolve when ( \kappa ) changes. By demonstrating these results in models of hard-core anyons and discussing realizable quantum simulation experiments, the authors provide both theoretical insights and potential practical pathways for exploring anyonic physics experimentally (Original article, 2022).

From a quantum governance perspective, this research offers critical insights into managing and controlling quantum states in systems with tunable exchange statistics—an emerging frontier in quantum technologies. The continuous transformation framework for tuning the statistical parameter ( \kappa ) provides a conceptual and operational tool for dynamically adjusting quantum system behavior, essential for the design of robust quantum simulators and information processors using anyons. Understanding the universal orthogonality catastrophe and how state overlaps decay as statistics shift informs how quantum protocols might be engineered to manage quantum coherence and distinguishability in practice, reducing error and enhancing control fidelity. Moreover, the notion of quantum speed limits linked to statistical parameter flows can guide governance frameworks on feasible rates of quantum operation changes, ensuring stable transitions without losing quantum information integrity. Consequently, this work underpins strategies for adaptive quantum control and secure quantum information architectures in systems governed by nontrivial particle statistics, crucial for advancing quantum governance policies that integrate both foundational physics and practical quantum simulation capabilities.

Reference:
Original article (2022). Quantum Alchemy and Universal Orthogonality Catastrophe in One-Dimensional Anyons.