Complete positivity and contextuality of quantum dynamics

TL;DR

This paper explores the fundamental properties of quantum dynamics, demonstrating how unitary dilations can characterize completely positive maps regardless of initial correlations, and extends the framework to include contextuality through measurement transfer matrices.

Contribution

It introduces a unitary dilation model for completely positive maps that works without initial correlation constraints and develops a measurement-chain formula to capture contextuality.

Findings

Unitary dilation models can characterize CP maps without initial correlation restrictions.

A measurement transfer matrix framework captures quantum contextuality.

The limitations of CP maps are discussed in the context of quantum dynamics.

Abstract

Positivity or the stronger notion of complete positivity, and contextuality are central properties of quantum dynamics. In this work, we demonstrate that a physical unitary-universe dilation model could be employed to characterize the completely positive map, regardless of the initial correlation condition. Particularly, the problem of initial correlation can be resolved by a swap operation. Furthermore, we discuss the physical essence of completely positive map and highlights its limitations. Then we develop the quantum measurement-chain formula beyond the framework of completely positive map in order to describe much broader quantum dynamics, and therein the property of contextuality could be captured via measurement transfer matrix.