Ergodic Dynamics in Iterated Quantum Protocols
Published:Dec 30, 2025 15:15
•1 min read
•ArXiv
Analysis
This paper explores the dynamics of iterated quantum protocols, specifically focusing on how these protocols can generate ergodic behavior, meaning the system explores its entire state space. The research investigates the impact of noise and mixed initial states on this ergodic behavior, finding that while the maximally mixed state acts as an attractor, the system exhibits interesting transient behavior and robustness against noise. The paper identifies a family of protocols that maintain ergodic-like behavior and demonstrates the coexistence of mixing and purification in the presence of noise.
Key Takeaways
- •Investigates measurement-induced nonlinear dynamics in iterated quantum protocols.
- •Identifies a protocol that generates globally chaotic, strongly mixing dynamics for pure states.
- •Analyzes the impact of noise and mixed initial states on the dynamics.
- •Introduces a notion of quasi-ergodicity to quantify robustness against noise.
- •Demonstrates the coexistence of statistical mixing and purification within a single iterated protocol.
Reference
“The paper introduces a practical notion of quasi-ergodicity: ensembles prepared in a small angular patch at fixed purity rapidly spread to cover all directions, while the purity gradually decreases toward its minimal value.”