Error-free interconversion of nonlocal boxes

TL;DR

This paper introduces an exact, adaptive protocol for converting extremal two-party, two-input nonlocal no-signaling boxes into any other extremal box, highlighting the versatility of no-signaling resources in different causal orders.

Contribution

It presents the first adaptive protocol for perfect interconversion of extremal nonlocal boxes, enabling flexible use of no-signaling resources in various causal configurations.

Findings

Exact interconversion protocol demonstrated

Expected number of boxes needed is finite

Shows usefulness of no-signaling boxes in different causal orders

Abstract

Understanding the structure of nonlocal correlations is important in many fields ranging from fundamental questions of physics to device-independent cryptography. We present a protocol that can convert extremal two-party--two-input nonlocal no-signaling boxes of any type into any other extremal two-party--two-input nonlocal no-signaling box perfectly. Our results are exact, and even though the number of required boxes cannot be determined in advance, their expected number is finite. Our protocol is adaptive and demonstrates for the first time the usefulness of using no-signaling boxes in different causal orders by the parties.