Resource theory of imaginarity: Quantification and state conversion

TL;DR

This paper develops a resource theory for the quantification and conversion of imaginarity in quantum systems, highlighting its role as a resource in quantum information and optical experiments.

Contribution

It introduces geometric and robustness measures for imaginarity, analyzes state conversion, and explores the complexity of real operations in optical setups.

Findings

Imaginarity can be quantified using geometric and robustness measures.

Any pair of real orthogonal pure states can be discriminated locally with real operations.

Imaginarity is a resource in optical quantum experiments.

Abstract

Complex numbers are widely used in both classical and quantum physics, and are indispensable components for describing quantum systems and their dynamical behavior. Recently, the resource theory of imaginarity has been introduced, allowing for a systematic study of complex numbers in quantum mechanics and quantum information theory. In this work we develop theoretical methods for the resource theory of imaginarity, motivated by recent progress within theories of entanglement and coherence. We investigate imaginarity quantification, focusing on the geometric imaginarity and the robustness of imaginarity, and apply these tools to the state conversion problem in imaginarity theory. Moreover, we analyze the complexity of real and general operations in optical experiments, focusing on the number of unfixed wave plates for their implementation. We also discuss the role of imaginarity for local state discrimination, proving that any pair of real orthogonal pure states can be discriminated via local real operations and classical communication. Our study reveals the significance of complex numbers in quantum physics, and proves that imaginarity is a resource in optical experiments.