Quantum Channels on Graphs: a Resonant Tunneling Perspective

TL;DR

This paper introduces a quantum-information-theoretic framework for analyzing quantum transport on graphs, revealing how resonant effects can enhance capacity and suppress noise in quantum channels within structured networks.

Contribution

It develops a novel method using the Redheffer star product to analyze resonant concatenation and super-activation in quantum channels on graphs, advancing understanding of quantum transport.

Findings

Resonant concatenation can suppress noise in quantum channels.

Super-activation of quantum capacity occurs through resonant effects.

The framework applies to quantum communication and control in structured environments.

Abstract

Quantum transport on structured networks is strongly influenced by interference effects, which can dramatically modify how information propagates through a system. We develop a quantum-information-theoretic framework for scattering on graphs in which a full network of connected scattering sites is treated as a quantum channel linking designated input and output ports. Using the Redheffer star product to construct global scattering matrices from local ones, we identify resonant concatenation, a nonlinear composition rule generated by internal back-reflections. In contrast to ordinary channel concatenation, resonant concatenation can suppress noise and even produce super-activation of the quantum capacity, yielding positive capacity in configurations where each constituent channel individually has zero capacity. We illustrate these effects through models exhibiting resonant-tunneling-enhanced transport. Our approach provides a general methodology for analyzing coherent information flow in quantum graphs, with relevance for quantum communication, control, and simulation in structured environments.