Perfect Wave Transfer in Continuous Quantum Systems

TL;DR

This paper explores perfect wave transfer in continuous quantum systems, highlighting the role of conformal invariance and spectral problems, and extends findings to interacting theories using bosonization.

Contribution

It demonstrates conditions for perfect wave transfer in continuous quantum systems and links conformal invariance to transfer efficiency, extending results to interacting theories.

Findings

Conformal invariance enables perfect wave transfer in continuous systems.

Solutions to inverse spectral problems characterize transfer in non-conformal systems.

Bosonization extends the results to interacting quantum theories.

Abstract

The transfer of information from one part of a quantum system to another is fundamental to the understanding and design of quantum information processing devices. In the realm of discrete systems such as spin chains, inhomogeneous networks have been engineered that allow for the perfect transfer of qubits from one end to the other. Here, by contrast, we investigate the perfect transfer of information in continuous systems, phrased in terms of wave propagation. A remarkable difference is found between systems that possess conformal invariance and those that do not. Systems in the first class enjoy perfect wave transfer (PWT), explicitly shown for one-particle excitations and anticipated in general. In the second class, those that exhibit PWT are characterized as solutions to an inverse spectral problem. As a concrete example, we demonstrate how to formulate and solve this problem for a prototypical class of bosonic theories, showing the importance of conformal invariance for these theories to enjoy PWT. Using bosonization, our continuum results extend to theories with interactions, broadening the scope of perfect information transfer to more general quantum systems.