The Deimginarity Cost of Quantum States

TL;DR

This paper introduces the concept of deimaginarity cost for quantum states, showing it equals the regularized relative entropy of imaginarity, providing an operational interpretation for this measure.

Contribution

It establishes the deimaginarity cost as equal to the regularized relative entropy of imaginarity, linking a resource measure to an operational task in quantum state transformation.

Findings

Deimaginarity cost equals the regularized relative entropy of imaginarity.

Operational interpretation of the relative entropy of imaginarity.

Analysis in the scenario of infinite copies and small error.

Abstract

Here we address a task denoted as deimaginarity, which is to transform a state into a real state with the aid of random covariant-free unitary operations. We consider the minimum cost of randomness required for deimaginarity in the scenario of infinite copies and suiciently small error, and we prove that the deimaginarity cost of a state $\rho$ is equal to its regularized relative entropy of imaginarity, which can be seen as an operational interpretation of the relative entropy of imaginarity.