Robust Decomposition of Quantum States

We show that quantum states over multiple subsystems can be recursively decomposed into states on one fewer subsystem and quantum operations that extend the state onto the omitted subsystem. This decomposition is robust in the sense that dephasing errors on subsystems between operations do not alter the marginal state on error-free subsystems. By restricting the form of these operations to a truncated cluster expansion, their classical simulation cost is reduced to the cost of simulating the maximal clusters. Such simulations provide direct access to independent statistical samples of observables and systematically improvable lower bounds on the von Neumann entropy, which together enable variational free energy minimization.