Optimal detection of dissipation in Lindbladian dynamics
This provides a practical method for detecting dissipative noise in experimentally implemented quantum dynamics, addressing a key challenge in quantum computing and simulation.
The paper tackles the problem of detecting dissipative noise in quantum dynamics by determining if observed time evolution is purely Hamiltonian or includes dissipation of at least a certain magnitude, and presents a randomized procedure with total evolution time O(ε⁻¹), which is information-theoretically optimal.
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.