Control of quantum noise: on the role of dilations

TL;DR

This paper explores how all finite-dimensional Markovian quantum systems can be represented by autonomous unitary dilations, emphasizing their control and decoupling, with novel constructions using a time-dependent Stinespring approach.

Contribution

It introduces a method to construct autonomous unitary dilations for Markovian quantum systems and analyzes their controllability and decoupling properties.

Findings

Every finite-dimensional Markovian quantum system has an autonomous unitary dilation.

Some dilations cannot be dynamically decoupled, affecting control strategies.

A new dilation construction uses a time-dependent Stinespring approach and clock Hamiltonian.

Abstract

We show that every finite-dimensional quantum system with Markovian (i.e., GKLS-generated) time evolution has an autonomous unitary dilation which can be dynamically decoupled. Since there is also always an autonomous unitary dilation which cannot be dynamically decoupled, this highlights the role of dilations in the control of quantum noise. We construct our dilation via a time-dependent version of Stinespring in combination with Howland's clock Hamiltonian and certain point-localised states, which may be regarded as a C*-algebraic analogue of improper bra-ket position eigenstates and which are hence of independent mathematical and physical interest.