Power of Quantum Measurement in Simulating Unphysical Operations

Difference between (a) quasi-probability decomposition and (b) measurement-controlled post-processing.

Abstract

The manipulation of quantum states through linear maps beyond quantum operations has many important applications in various areas of quantum information processing. Current methods simulate unphysical maps by sampling physical operations, but in a classical way. In this work, we show that using quantum measurement in place of classical sampling leads to lower simulation costs for general Hermitian-preserving maps. Remarkably, we establish the equality between the simulation cost and the well-known diamond norm, thus closing a previously known gap and assigning diamond norm a universal operational meaning as a map’s simulability. We demonstrate our method in two applications closely related to error mitigation and quantum machine learning, where it exhibits a favorable scaling. These findings highlight the power of quantum measurement in simulating unphysical operations, in which quantum interference is believed to play a vital role. Our work paves the way for more efficient sampling techniques and has the potential to be extended to more quantum information processing scenarios.

Publication
arXiv.2309.09963
Lei Zhang
Lei Zhang
PhD Student

I obtained my BMath in AMath, CO & joint PMath from the University of Waterloo. My research interests include quantum information theory and quantum machine learning.

Xin Wang
Xin Wang
Associate Professor

The main focus of my research is to better understand the limits of information processing with quantum systems and the power of quantum artificial intelligence.