Some notes on the robustness of k-coherence and k-entanglement

TL;DR

This paper proves the equivalence of two measures of k-coherence and k-entanglement for pure states, providing efficient, closed-form formulas for their computation and addressing existing conjectures in quantum resource quantification.

Contribution

It establishes the equality of robustness measures for pure states and introduces computable formulas, resolving prior conjectures in quantum coherence and entanglement quantification.

Findings

The robustness measures are equal for pure states.

Closed-form expressions for the measures are derived.

The results confirm conjectures in the literature.

Abstract

We show that two related measures of k-coherence, called the standard and generalized robustness of k-coherence, are equal to each other when restricted to pure states. As a direct application of the result, we establish an equivalence between two analogous measures of Schmidt rank k-entanglement for all pure states. This answers conjectures raised in the literature regarding the evaluation of the quantifiers, and facilitates an efficient quantification of pure-state resources by introducing computable closed-form expressions for the two measures.