Witnessing Quantum Speedup through Mutual Information

Abstract

AbstractAchieving dynamical speedup of evolution in an open quantum system plays a key role in many technological applications. However, how to detect quantum speedup is unclear. In this work, a method to witness quantum speedup through the measure of the mutual information is presented. It is shown that the speed of evolution of a quantum system, can be witnessed by calculating the mutual information variation, whose increase is a clear signature of dynamical speedup. The result is explained by considering the time evolution of two qubits under a one‐sided noisy channel, finding out that the mechanism for the quantum speedup is closely associated with the total exchange of information between the system and its environment, which can be expressed by the variation of mutual information. Quantitatively, the average speed of evolution is shown proportional to the average variation of the mutual information in an interval of time. The conclusion can not only explain why the quantum entanglement (or quantum coherence) and the classical correlation are neither necessary nor sufficient to speed up the quantum evolution, but also give a vital way of detecting quantum speedup in realistic environments.