Open quantum dynamics without Complete Positivity: a criticism

TL;DR

This paper critically examines the necessity of complete positivity in open quantum dynamics, highlighting limitations of alternative domain restriction approaches through isotropic state examples.

Contribution

It challenges the common assumption of complete positivity as essential, revealing weaknesses in compatibility-based approaches for higher-dimensional systems.

Findings

Domain restrictions become more severe with system dimension

Compatibility-based approaches have intrinsic weaknesses

Complete positivity may not be a necessary condition

Abstract

The requirement of complete positivity is very often regarded as a fundamental consistency condition for the description of open quantum dynamics. We critically examine this requirement and discuss both its physical motivations and its limitations. We analyze proposals based on restricting the domain of non-completely positive maps to subsets of compatible initial states. Using isotropic states as a concrete example, we show that such domain restrictions become increasingly severe with growing system dimension, revealing an intrinsic weakness of the compatibility-based approach.