Wave-Particle-Mixedness Relationships Based on lp-norm Coherence

TL;DR

This paper explores the fundamental relationships among wave, particle, and mixedness properties of quantum states using lp-norm coherence, establishing new tradeoff bounds that deepen understanding of quantum state characteristics.

Contribution

It introduces a novel measure of particle property based on l2-norm coherence differences and derives new tradeoff relations involving lp-norm coherence for 1<= p < 2.

Findings

Established tradeoff relations between wave, particle, and mixedness properties.

Provided bounds of lp-norm coherence related to l2-norm coherence.

Unified understanding of quantum state properties covering previous results.

Abstract

We investigate the relationships among the wave property, particle property and mixedness of quantum states based on the lp-norm coherence. By conforming that the lp-norm coherence is an appropriate measure of wave property and introducing a measure of particle property based on the differences between the maximal l2-norm coherence and the general l2-norm coherence, we present tradeoff relationships among the wave, particle and mixedness of quantum states. For 1<= p <2, we establish two kinds of tradeoffs of the wave, particle and mixedness with respect to the upper and lower bounds of the lp-norm coherence given by the l2-norm coherence. These trade relations give rise to compressive understanding of the intrinsic connections among the wave, particle and mixedness of quantum states, and cover some existing results as particular ones.