QUANTUMNESS OF ENSEMBLE FROM NO-BROADCASTING PRINCIPLE

Abstract

Quantum information, though not precisely defined, is a fundamental concept of quantum information theory which predicts many fascinating phenomena and provides new physical resources. A basic problem is to recognize the features of quantum systems responsible for those phenomena. One of these important features is that non-commuting quantum states cannot be broadcast: two copies cannot be obtained out of a single copy, not even reproduced marginally on separate systems. We focus on the difference in information content between one copy and two copies, which is a basic manifestation of the gap between quantum and classical information. We show that if the chosen information measure is the Holevo quantity, the difference between the information content of one copy and two copies is zero if and only if the states can be broadcast. We propose a new approach in defining measures of quantumness of ensembles based on the difference in information content between the original ensemble and the ensemble of duplicated states. We comment on the permanence property of quantum states and the recently introduced superbroadcasting operation. We also provide an appendix where we discuss the status of quantum information in quantum physics, based on the so-called isomorphism principle.