Quantifying imaginarity in terms of pure-state imaginarity

TL;DR

This paper introduces two new theoretical methods to quantify the role of complex numbers in quantum systems, advancing the resource theory of imaginarity in quantum information science.

Contribution

It develops convex roof and pure-state minimization methods for measuring imaginarity, and applies these to state conversion problems.

Findings

Two quantifiers of imaginarity are proposed.

Methods are inspired by resource theories of entanglement and coherence.

Applications include analyzing state conversion in imaginarity resource theory.

Abstract

Complex numbers are widely used in quantum physics and are indispensable components for describing quantum systems and their dynamical behavior. The resource theory of imaginarity has been built recently, enabling a systematic research of complex numbers in quantum information theory. In this work, we develop two theoretical methods for quantifying imaginarity, motivated by recent progress within resource theories of entanglement and coherence. We provide quantifiers of imaginarity by the convex roof construction and quantifiers of the imaginarity by the least imaginarity of the input pure states under real operations. We also apply these tools to study the state conversion problem in resource theory of imaginarity.