Classicality from Quantum Stochastic Processes

TL;DR

This paper develops a theoretical framework connecting quantum stochastic processes to classicality, using semidefinite programming and fixed point analysis to distinguish classical from quantum behaviors.

Contribution

It introduces a new semidefinite programming approach to characterize quantum channels and their fixed points, expanding the understanding of classicality emergence from quantum systems.

Findings

A semidefinite program characterizes quantum channels separating core and decaying parts.

A characterization of channels based on fixed points for the separable case.

Construction of quantum simulations of polyhedral cones.

Abstract

I develop a theory of classicality from quantum systems. This theory stems from the study of classical and quantum stationary stochastic processes. The stochastic processes are characterized by polyhedral (classical) and semidefinite representative (quantum) cones. Based on a previous result by the author I expand the study of fixed points from quantum channels. I give a semidefinite program that characterizes a quantum channel separating into a core and a part that decays with many iterations. In general, the solution is non-separable in the space it is defined. I present a characterization of channels in terms of their fixed points for the separable case. A quantum simulation of a polyhedral cone can then be constructed.