Of Local Operations and Physical Wires

TL;DR

This paper unifies entanglement, discord, and coherence into a single resource theory based on local operations and the quantum nature of communication channels, revealing new operational insights.

Contribution

It introduces a generalized resource theory focusing on coherence in the connecting wire, encompassing entanglement and discord as different aspects of this framework.

Findings

Identifies coherence in the connecting wire as a key resource.

Derives a closed-form of free operations for discord-like resources.

Explains phenomena like entanglement without particle entanglement.

Abstract

In this work (multipartite) entanglement, discord and coherence are unified as different aspects of a single underlying resource theory defined through simple and operationally meaningful elemental operations. This is achieved by revisiting the resource theory defining entanglement, Local Operations and Classical Communication (LOCC), placing the focus on the underlying quantum nature of the communication channels. Taking the natural elemental operations in the resulting generalization of LOCC yields a resource theory that singles out coherence in the wire connecting the spatially separated systems as an operationally useful resource. The approach naturally allows to consider a reduced setting as well, namely the one with only the wire connected to a single quantum system, which leads to discord-like resources. The general form of free operations in this latter setting is derived and presented as a closed form. We discuss in what sense the present approach defines a resource theory of quantum discord and in which situations such an interpretation is sound -- and why in general discord is not a resource. This unified and operationally meaningful approach makes transparent many features of entanglement that in LOCC might seem surprising, such as the possibility to use a particle to entangle two parties, without it ever being entangled with either of them, or that there exist different forms of multipartite entanglement.