Time-Energy Measure for Quantum Processes

TL;DR

This paper introduces a new measure for quantum processes that quantifies the tradeoff between time and energy, providing bounds and exact values for certain channels, and reveals that quantum information erasure is more resource-intensive than classical.

Contribution

It proposes a novel time-energy measure for quantum channels, deriving bounds and exact values for specific classes, and compares quantum and classical information erasure resources.

Findings

Exact time-energy measure for some channels including depolarizing

Quantum information erasure requires more resources than classical

Derived bounds for general quantum channels

Abstract

Quantum mechanics sets limits on how fast quantum processes can run given some system energy through time-energy uncertainty relations, and they imply that time and energy are tradeoff against each other. Thus, 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 can obtain the exact value of the time-energy measure. One consequence of our result is that erasing quantum information requires $\sqrt{(n+1)/n}$ times more time-energy resource than erasing classical information, where $n$ is the system dimension.