Measuring time-energy resources for quantum processes

Abstract

The speed of any quantum process is limited by quantum mechanics via time-energy uncertainty relations and they imply that time and energy are tradeoff with each other. As such, we propose to measure the time-energy as a single unit for quantum channels. We consider a time-energy measure for quantum channels and compute lower and upper bounds of it using the channel Kraus operators. For a special class of channels (which includes the depolarizing channel), we obtain the exact value of the time-energy measure. Our result can be used to compare the time-energy resources of similar quantum processes. In particular, we show that erasing quantum information requires √(n + 1)/n) times more time-energy resource than erasing classical information, where n is the system dimension. This work is published in [1].