Convex ordering and quantification of quantumness

TL;DR

This paper introduces a convex ordering framework for quantum states that unambiguously quantifies quantum effects by leveraging classical state definitions, applicable to quantum optics and information theory.

Contribution

It proposes a novel convex ordering method based on algebraic classical states, resolving ambiguities in quantumness measures and generalizing to classical operations.

Findings

Provides a new convex ordering technique for quantum states.

Clarifies quantumness quantification using classical state structures.

Applies the method to quantum optics and information scenarios.

Abstract

The characterization of physical systems requires a comprehensive understanding of quantum effects. One aspect is a proper quantification of the strength of such quantum phenomena. Here, a general convex ordering of quantum states will be introduced which is based on the algebraic definition of classical states. This definition resolves the ambiguity of the quantumness quantification using topological distance measures. Classical operations on quantum states will be considered to further generalize the ordering prescription. Our technique can be used for a natural and unambiguous quantification of general quantum properties whose classical reference has a convex structure. We apply this method to typical scenarios in quantum optics and quantum information theory to study measures which are based on the fundamental quantum superposition principle.