Power of quantum measurement in simulating unphysical operations

TL;DR

This paper demonstrates that quantum measurement can more efficiently simulate unphysical Hermitian-preserving maps than classical sampling, establishing a direct link between simulation cost and the diamond norm, with applications in error mitigation and quantum machine learning.

Contribution

It introduces a measurement-based simulation method that reduces costs and proves the diamond norm's operational significance for all Hermitian-preserving maps.

Findings

Measurement-based simulation has lower costs than classical methods.

Simulation cost equals the diamond norm for Hermitian-preserving maps.

Method shows favorable scaling in error mitigation and quantum machine learning.

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 according to classically determined probability distributions. In this work, we show that using quantum measurement instead 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 for all Hermitian-preserving maps. 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.