Duality as a Feasible Physical Transformation

TL;DR

This paper proposes a practical method to implement duality transformations as physical operations in quantum simulations, enabling laboratory realization of dual states with identical observable physics, demonstrated on Abelian lattice models.

Contribution

It introduces a feasible scheme to realize duality transformations as physical operations in quantum systems, bridging a gap between mathematical dualities and experimental quantum simulation.

Findings

Duality transformations can be implemented as sequences of unitaries and measurements.

The scheme is demonstrated on Abelian lattice models.

Dual states exhibit the same observable physics in experiments.

Abstract

Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous advantages for the study of many-body physics. In this work, we suggest a method which shall introduce them to the world of quantum simulation too: a feasible scheme for implementing duality transformations as physical operations, mapping between dual quantum states showing the same observable physics, rather than just a mathematical trick. Demonstrating with Abelian lattice models, we show how duality transformations could be implemented in the laboratory as sequences of single- and two-body operations - unitaries and measurements.