Measures of imaginarity and quantum state order

TL;DR

This paper explores measures of the 'imaginarity' of quantum states using resource theory, examining how quantum channels affect state order, with a focus on single-qubit systems and various mathematical measures.

Contribution

It introduces and analyzes measures of quantum state imaginarity within resource theory and studies the impact of quantum channels on state order for single-qubits.

Findings

Different measures of imaginarity are characterized and compared.

Quantum channels can alter the order of quantum states.

The study provides insights into the resource theory of imaginarity.

Abstract

Complex numbers are widely used in both classical and quantum physics, and play an important role in describing quantum systems and their dynamical behavior. In this paper we study several measures of imaginarity of quantum states in the framework of resource theory, such as the measures based on $l_{1}$ norm, and convex function, etc. We also investigate the influence of the quantum channels on quantum state order for a single-qubit.