Optimal detection of dissipation in Lindbladian dynamics

TL;DR

This paper presents an optimal randomized method for detecting dissipation in quantum systems governed by Lindbladian dynamics, using only observed time evolution, with guarantees under certain bounded conditions.

Contribution

It introduces a practically feasible, optimal procedure for identifying dissipation in quantum dynamics from black-box access, improving on prior methods.

Findings

The procedure uses total evolution time proportional to 1/epsilon.

It is information-theoretically optimal.

Works under bounded strength and locality assumptions.

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 $\epsilon$ in normalized Frobenius norm. We give a randomized procedure that solves this task using total evolution time $\mathcal{O}(\epsilon^{-1})$, 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.