Distributed Private Randomness Distillation

TL;DR

This paper develops a resource theory for private randomness extraction in distributed quantum systems, introducing new concepts and operational interpretations, and revealing that local noise can enhance randomness extraction.

Contribution

It introduces the notion of independent random bits, the concept of Virtual Quantum State Merging, and provides an operational interpretation for reverse coherent information.

Findings

Local noise can boost randomness extraction.

Operational interpretation of reverse coherent information as private randomness.

Achievable rate regions for bipartite private randomness extraction.

Abstract

We develop the resource theory of private randomness extraction in the distributed and device-dependent scenario. We begin by introducing the notion of independent random bits, which are bipartite states containing ideal private randomness for each party, and motivate the natural set of free operations. As a conceptual tool, we introduce Virtual Quantum State Merging, which is essentially the flip side of Quantum State Merging, without communication. We focus on the bipartite case and find the rate regions achievable in different settings. Surprisingly, it turns out that local noise can boost randomness extraction. As a consequence of our analysis, we resolve a long-standing problem by giving an operational interpretation for the reverse coherent information (up to a constant term $\log d$) as the number of private random bits obtained by sending quantum states from one honest party (server) to another one (client) via the eavesdropped quantum channel.