Fig. 1: Exemplary illustration of quantum hypothesis testing.

a Binary hypothesis testing process for dynamics discrimination. The binary hypotheses are H₀ and H₁ with respective prior probabilities q₀ and q₁. A known initial state evolves under hypothesis Hamiltonian H₀ (or H₁) to the final state ρ₀ (or ρ₁). Quantum measurement M is performed to decide one of the hypotheses. The coherent control strategy and noise engineering technology are considered as resources to enhance the effectiveness of decision-making. b, c Depict scenarios in which the two to-be-distinguished dynamics are influenced by Hamiltonian-independent noise and Hamiltonian-dependent noise, respectively. While Hamiltonian-independent noise can decrease the trace distance of the final states, i.e., \({D}_{{{\rm{tr}}}}^{\,{\mbox{noise}}\,} < {D}_{{{\rm{tr}}}}^{\,{\mbox{uni}}\,}\), thereby reducing the success probability, Hamiltonian-dependent noise has the inherent potential of increasing the trace distance, such that \({D}_{{{\rm{tr}}}}^{\,{\mbox{noise}}\,} > {D}_{{{\rm{tr}}}}^{\,{\mbox{uni}}\,}\), and thus enhancing the success probability.