Tomographically-nonlocal entanglement

TL;DR

This paper investigates how entanglement behaves in theories where local measurements cannot fully determine the global state, revealing two types of entanglement with distinct operational uses and clarifying puzzling features in such nonlocal theories.

Contribution

It introduces a framework distinguishing two forms of entanglement in tomographically nonlocal theories and analyzes their operational significance, especially in relation to quantum information tasks.

Findings

Tomographically-nonlocal entanglement is not useful for Bell nonlocality, steering, or teleportation.

It is sufficient for dense coding and secure data hiding.

The framework explains puzzling features of entanglement under superselection rules.

Abstract

Entanglement is a central and subtle feature of quantum theory, whose structure and operational behavior can change dramatically when additional physical constraints, such as symmetries or superselection rules, are imposed. Such constraints can give rise to striking and counter-intuitive phenomena, including local broadcasting of entangled states and failures of entanglement monogamy. These effects naturally arise in tomographically nonlocal theories (like real quantum theory, twirled worlds, or fermionic quantum theory), where composite systems possess holistic degrees of freedom that are inaccessible to local measurements. In this work, we study entanglement in such theories within the framework of generalized probabilistic theories. We show that the failure of tomographic locality leads to two qualitatively distinct forms of entanglement, which we term $\textit{tomographically-local}$ entanglement and $\textit{tomographically-nonlocal}$ entanglement. We analyze the operational consequences of this distinction, proving that tomographically-nonlocal entanglement is useless for Bell nonlocality, steering, and teleportation, but sufficient for dense coding and perfectly secure data hiding. This framework clarifies the origin of several previously puzzling features of entanglement that arise when tomographic locality fails, as can happen even in quantum theory when one considers fermions or fundamental superselection rules.