The classicality and quantumness of a quantum ensemble

TL;DR

This paper introduces measures of classicality and quantumness for quantum ensembles, linking classicality to cloning ability and quantumness to QKD security, providing insights into quantum information processing.

Contribution

It defines new quantitative measures for classicality and quantumness of quantum ensembles and explores their implications for quantum cloning and quantum key distribution security.

Findings

Classicality is related to the ensemble's clonability.

Quantumness determines the security level of QKD protocols.

Quantumness sets the lower bound of error rate in QKD.

Abstract

In this paper, we investigate the classicality and quantumness of a quantum ensemble. We define a quantity called classicality to characterize how classical a quantum ensemble is. An ensemble of commuting states that can be manipulated classically has a unit classicality, while a general ensemble has a classicality less than 1. We also study how quantum an ensemble is by defining a related quantity called quantumness. We find that the classicality of an ensemble is closely related to how perfectly the ensemble can be cloned, and that the quantumness of an ensemble is essentially responsible for the security of quantum key distribution(QKD) protocols using that ensemble. Furthermore, we show that the quantumness of an ensemble used in a QKD protocol is exactly the attainable lower bound of the error rate in the sifted key.