Geometric-Like imaginarity: quantification and state conversion

TL;DR

This paper introduces a new geometric-like measure of imaginarity in quantum physics, demonstrating its stability under noise and its application in optimizing state transformation probabilities.

Contribution

It proposes a novel geometric-like measure of imaginarity that outperforms traditional measures in stability and provides explicit formulas for state transformation probabilities.

Findings

The geometric-like measure shows smaller decay under noisy channels.

It enables calculation of optimal transformation probabilities.

The measure is more stable than previous imaginarity measures.

Abstract

From the perspective of resource-theoretic approach, this study explores the quantification of imaginary in quantum physics. We propose a well defined measure of imaginarity, the geometric-like measure of imaginarity. Compared with the usual geometric imaginarity measure, this geometric-like measure of imaginarity exhibits smaller decay difference under quantum noisy channels and higher stability. As applications, we show that both the optimal probability of state transformations from a pure state to an arbitrary mixed state via real operations, and the maximal probability of stochastic-approximate state transformations from a pure state to an arbitrary mixed state via real operations with a given fidelity $f$, are given by the geometric-like measure of imaginarity.