The quantum network as an environment

TL;DR

This paper introduces a novel cavity or Belief Propagation method to compute the influence functional in quantum networks with tree-like topology, enabling analysis of quantum environments and disorder effects.

Contribution

It develops a new BP-based approach to determine the influence functional in quantum networks, extending the analysis to harmonic oscillators and disorder effects.

Findings

BP method successfully computes influence functionals for harmonic oscillator networks

The approach handles disorder and replica symmetry considerations

Fixed points of the BP equations are characterized for specific network topologies

Abstract

quantum system interacting with other quantum systems experiences these other systems asan effective environment. The environment is the result of integrating out all the other degrees of freedom in the network, and can be represented by a Feynman-Vernon influence functional (IF)acting on system of interest. A network is characterized by the constitutive systems, how they interact, and the topology of those interactions. Here we show that for networks having the topology of locally tree-like graphs, the Feynman-Vernon influence functional can be determined in a new version of the cavity or Belief Propagation (BP) method. In the BP update stage, cavity IFs are mapped to cavity IFs, while in the BP output stage cavity IFs are combined to output IFs. We compute the fixed point of of this version of BP for harmonic oscillator systems interacting uniformly. We discuss Replica Symmetry and the effects of disorder in this context.