Deterministic twirling with low resources

Twirling operations, which average a quantum state with respect to a unitary subgroup, have become a frequently-employed tool in quantum information processing. We investigate the efficient implementation of twirling operations with minimal resources, without necessitating the ability to perform all possible unitary operations on the quantum system of interest. We present a general algebraic method allowing us to choose a set of - typically very few - unitary operators which, when applied randomly and repeatedly, produce the given twirling operation exponentially quickly. The method is applied to twirling operations for bipartite quantum systems with respect to the unitary group U(d)⊗U(d), an essential ingredient in entanglement distillation protocols. In particular, we provide a complete classification of sets of unitary operators capable of performing twirling on two qubits. Moreover, we construct a generic set containing at most three unitary operators achieving the twirling operation for a general two-qudit system. •We present a method of twirling based on Random Unitary Operations (RUOs).•RUOs allow entanglement distillation to be performed with low experimental resources.•We give a set of necessary and sufficient conditions which allow two-qubit twirling.•We give a general RUO which performs two-qudit twirling in any dimension.