Information flow and error scaling for fully-quantum control

TL;DR

This paper demonstrates that the quantum channel capacity determines the scaling of control error in fully-quantum control systems, emphasizing the importance of optimizing quantum information flow for improved control accuracy.

Contribution

It establishes a direct link between quantum channel capacity and control error scaling, providing analytical and numerical results for qubits and Bosonic modes.

Findings

Quantum capacity bounds control error scaling.

Optimizing quantum information flow minimizes control errors.

Results applicable to various quantum platforms.

Abstract

The optimally designed control of quantum systems is playing an increasingly important role to engineer novel and more efficient quantum technologies. Here, in the scenario represented by controlling an arbitrary quantum system via the interaction with an another optimally initialized auxiliary quantum system, we show that the quantum channel capacity sets the scaling behaviour of the optimal control error. Specifically, we prove that the minimum control error is ensured by maximizing the quantum capacity of the channel mapping the initial control state into the target state of the controlled system, i.e., optimizing the quantum information flow from the controller to the system to be controlled. Analytical results, supported by numerical evidences, are provided when the systems and the controller are either qubits or single Bosonic modes and can be applied to a very large class of platforms for controllable quantum devices.