Macro-to-micro quantum mapping and the emergence of nonlinearity

TL;DR

This paper develops a framework for mapping between macro and micro descriptions in quantum systems, revealing how nonlinear dynamics can emerge from linear quantum evolution, with applications to state discrimination.

Contribution

It introduces a method to assign microscopic quantum states consistent with macroscopic constraints using coarse-graining maps, enabling analysis of nonlinear effects.

Findings

Effective nonlinear dynamics can emerge from linear quantum evolution.

The approach applies even when the system-environment split is ambiguous.

Demonstrated in a state discrimination task.

Abstract

As a universal theory of physics, quantum mechanics must assign states to every level of description of a system -- from a full microscopic description, all the way up to an effective macroscopic characterization -- and also to describe the interconnections among them. Assuming that we only have a coarse-grained access to a physical system, here we show how to assign to it a microscopic description that abides by all macroscopic constraints. In order to do that, we employ general coarse-graining maps, allowing our approach to be used even when the split between system and environment is not obvious. As a by-product, we show how effective nonlinear dynamics can emerge from the linear quantum evolution, and we readily apply it to a state discrimination task.