Annealing Approach to Quantum Tomography

Annealing approach to tomography is theoretically proposed. First, based on the maximum entropy principle, we introduce classical parameters to combine quantum models (or states) given a prior for potentially representing the unknown target state. Then, we formulate the tomography as an optimization problem on the classical parameters, by employing relative entropy of the parametrized state with the target state as the objective function to be minimized. We show that the objective function is physically implementable, in a theoretical sense at least, as an effective Hamiltonian to be induced by physical interactions of the system with environment systems being prepared in the target state. Corollary, applying annealing to the effective Hamiltonian, we can execute tomography by obtaining the ground state that gives the optimal parameters.