A Quantum Law of Requisite Variety

The Law of Requisite Variety was the first attempt to quantify the ability of a controller to shield information-processing systems against error sources. It was then rediscovered in classical control theory, complexity science and computational mechanics. I here extend it to the quantum domain, establishing information-theoretic limits to the controllability of open quantum systems in terms of the resources available to the controller, quantum coherence and correlations. I also introduce a measure of controllability to capture the influence exerted on a system by a controlling device. I verify the result by implementing a control protocol in the IBM 5-qubit chip ``ibmqx4''.
LA-UR-18-29964