Optimal detection of dissipation in Lindbladian dynamics

2026-03-18

AI Summary

This work addresses the problem of distinguishing whether the dynamics of a black-box quantum system arise from unitary Hamiltonian evolution or from a Lindbladian generator containing dissipation of at least magnitude ε, using only observations of its time evolution. Under the assumptions of time-independent, bounded-strength, and constant-locality dissipation, the authors propose an efficient detection algorithm based on randomized measurements and the Frobenius norm. This method achieves information-theoretically optimal performance for dissipative detection, requiring only a total evolution time of O(ε⁻¹)—a significant improvement over prior approaches. The result provides a theoretically optimal and experimentally practical tool for rapidly identifying quantum noise in real-world settings.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Distributed Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Security and Privacy: Large-scale security measurements

Abstract

Experimental implementations of Hamiltonian dynamics are often affected by dissipative noise arising from interactions with the environment. This raises the question of whether one can detect the presence or absence of such dissipation using only access to the observed time evolution of the system. We consider the following decision problem: given black-box access to the time-evolution channels $e^{t\mathcal{L}}$ generated by an unknown time-independent Lindbladian $\mathcal{L}$, determine whether the dynamics are purely Hamiltonian or contain dissipation of magnitude at least $ε$ in normalized Frobenius norm. We give a randomized procedure that solves this task using total evolution time $\mathcal{O}(ε^{-1})$, which is information-theoretically optimal. This guarantee holds under the assumptions that the Lindblad generator has bounded strength and its dissipative part is of constant locality with bounded degree. Our work provides a practical method for detecting dissipative noise in experimentally implemented quantum dynamics.

Problem

• dissipation detection
• Lindbladian dynamics
• Hamiltonian dynamics
• quantum noise
• time evolution

Innovation

• Lindbladian dynamics
• dissipation detection
• quantum noise characterization
• optimal query complexity
• Hamiltonian vs dissipative dynamics