The Global versus Local Hamiltonian Description of Quantum Input-Output Theory

TL;DR

This paper derives a global Hamiltonian framework for quantum input-output systems from local descriptions, extending the theory to Fermi systems and providing a unified approach for quantum networks.

Contribution

It introduces a new simple method to obtain the global Hamiltonian from local descriptions and extends quantum feedback network theory to Fermi systems.

Findings

Global Hamiltonian as singular perturbation of free translation operator

Extension of quantum feedback networks to Fermi systems

Unified description of quantum input-output systems

Abstract

The aim of this paper is to derive the global Hamiltonian form for a quantum system and bath, or more generally a quantum network with multiple quantum input field connections, based on the local descriptions. We give a new simple argument which shows that the global Hamiltonian for a single Markov component arises as the singular perturbation of the free translation operator. We show that the Fermi analogue takes an equivalent form provided the parity of the coefficients is correctly specified. This allows us to immediately extend the theory of quantum feedback networks to Fermi systems.