Optimal universal bounds for waves with varied coherence based on supremum and infimum coherence spectra

TL;DR

This paper develops a majorization-based framework to establish optimal universal bounds for wave observables with varied coherence, using supremum and infimum coherence spectra to provide the tightest possible constraints.

Contribution

It introduces a novel majorization-based theory and an algorithm to compute supremum and infimum coherence spectra for bounding wave observables.

Findings

Supremum and infimum spectra provide optimal universal bounds.

The bounds are attained by maximal and minimal coherence spectra.

An algorithm for computing these spectra is proposed.

Abstract

We establish a majorization-based theory for bounding observables of waves with varied coherence. For any measurement, exact bounds are attained by the maximal and minimal elements in the set of input coherence spectra. The set's supremum and infimum, which may lie outside the set, provide optimal universal bounds: any alternative spectrum yielding universal bounds produces weaker constraints. We present an algorithm to compute the supremum and infimum, and prove that they lie either at singular boundary points or strictly outside the set of coherence spectra.