Schmidt-number robustness as a unified quantifier of high dimensional entanglement in Buscemi nonlocality

TL;DR

This paper introduces a unified robustness measure for high-dimensional entanglement that applies to states, measurements, and teleportation devices, linking them through a common resource quantifier in Buscemi nonlocality.

Contribution

It develops a convex framework and robustness monotones that unify the resource theory of high-dimensional entanglement across different quantum objects.

Findings

Schmidt-number robustness equals the maximum robustness of derived measurements and instruments.

A single robustness measure governs high-dimensional entanglement in various quantum objects.

Operational interpretation relates robustness to advantage in entanglement-assisted state discrimination.

Abstract

High-dimensional entanglement, captured by the Schmidt number, underpins advantages in quantum information tasks, yet a unified resource-theoretic description across different Buscemi-type operational objects has been missing. Here we develop a convex framework that treats bipartite states, distributed measurements, and teleportation instruments generated from shared entanglement on equal footing. For a fixed Schmidt-number threshold k, we introduce robustness-based monotones for each class of objects and prove a quantitative collapse: the Schmidt-number robustness of a bipartite state coincides with the maximal robustness achievable by any distributed measurement or teleportation instrument derived from that state. Consequently, within Buscemi-type operational frameworks, these objects do not carry independent high-dimensional resources but are governed by a single robustness-based monotone. We further provide a direct operational interpretation by relating this unique quantifier to the optimal advantage in entanglement-assisted state discrimination games. Our results complete a unified resource-theoretic characterization of high-dimensional entanglement across states, measurements, and quantum devices.