Measures from conical 2-designs depend only on two constants

TL;DR

This paper demonstrates that many quantum measures derived from conical 2-designs are fully characterized by just two positive constants, simplifying their analysis and application in quantum information tasks.

Contribution

It shows that a broad class of quantum measures from conical 2-designs depend only on two constants, providing a unified and simplified framework.

Findings

Quantum measures depend only on two constants.

Examples include entropic uncertainty, coherence, and entanglement criteria.

Simplifies analysis of quantum measurements.

Abstract

Quantum measurements are important tools in quantum information, represented by positive, operator-valued measures. A wide class of symmetric measurements is given via generalized equiangular measurements that form conical 2-designs. We show that only two positive constants are needed to fully characterize a variety of important quantum measures constructed from such operators. Examples are given for entropic uncertainty relations, the Brukner-Zeilinger invariants, quantum coherence, quantum concurrence, and the Schmidt-number criterion for entanglement detection.