On the Debate Concerning the Proper Characterisation of Quantum Dynamical Evolution

TL;DR

This paper discusses the debate over whether quantum dynamical evolution should include not completely positive (NCP) maps, proposing that NCP maps can be viewed as linear extensions of partially defined CP maps, broadening the understanding of quantum evolution.

Contribution

It clarifies the role of NCP maps in quantum dynamics, proposing they are linear extensions of partial CP maps, thus offering a new perspective on quantum evolution frameworks.

Findings

NCP maps can be understood as linear extensions of partial CP maps.

Allowing NCP maps broadens the scope of quantum dynamical evolution.

The debate over CP vs. NCP maps is addressed with a new interpretative framework.

Abstract

There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps. Despite the reasonableness of the arguments for complete positivity, we argue that NCP maps should be allowed, with a qualification: these should be understood, not as reflecting 'not completely positive' evolution, but as linear extensions, to a system's entire state space, of CP maps that are only partially defined. Beyond the domain of definition of a partial-CP map, we argue, much may be permitted.