Towards resource theory of coherence in distributed scenarios

TL;DR

This paper introduces a resource theory framework for quantum coherence in distributed systems, focusing on local incoherent operations and classical communication, and explores its implications for tasks like coherence distillation, teleportation, and state merging.

Contribution

It defines a new class of operations (LICC) for distributed coherence and shows that the larger class of separable incoherent operations has a simple form, advancing the understanding of coherence resources.

Findings

Separable incoherent operations have a simple mathematical form.

The approach applies to tasks like assisted coherence distillation, teleportation, and state merging.

Results are expected to extend to other coherence concepts in the literature.

Abstract

The search for a simple description of fundamental physical processes is an important part of quantum theory. One example for such an abstraction can be found in the distance lab paradigm: if two separated parties are connected via a classical channel, it is notoriously difficult to characterize all possible operations these parties can perform. This class of operations is widely known as local operations and classical communication (LOCC). Surprisingly, the situation becomes comparably simple if the more general class of separable operations is considered, a finding which has been extensively used in quantum information theory for many years. Here, we propose a related approach for the resource theory of quantum coherence, where two distant parties can only perform measurements which do not create coherence and can communicate their outcomes via a classical channel. We call this class local incoherent operations and classical communication (LICC). While the characterization of this class is also difficult in general, we show that the larger class of separable incoherent operations (SI) has a simple mathematical form, yet still preserving the main features of LICC. We demonstrate the relevance of our approach by applying it to three different tasks: assisted coherence distillation, quantum teleportation, and single-shot quantum state merging. We expect that the results obtained in this work also transfer to other concepts of coherence which are discussed in recent literature. The approach presented here opens new ways to study the resource theory of coherence in distributed scenarios.