Resource theory of quantum scrambling

Quantum chaos has become a cornerstone of physics through its many applications. One trademark of quantum chaotic systems is the spread of local quantum information, which physicists call scrambling. In this work, we introduce a mathematical definition of scrambling and a resource theory to measure it. We also describe two applications of this theory. First, we use our resource theory to provide a bound on magic, a potential source of quantum computational advantage, which can be efficiently measured in experiment. Second, we also show that scrambling resources bound the success of Yoshida's black hole decoding protocol.

Automated summary

Quantum chaos, characterized by the spread of local quantum information called scrambling, has found various applications in physics. This work introduces a mathematical definition of scrambling and a resource theory to measure it, along with two applications. Firstly, the resource theory is used to establish a bound on magic, a potential source of quantum computational advantage that can be efficiently measured in experiments. Secondly, it is shown that scrambling resources limit the success of Yoshida's black hole decoding protocol.