Entanglement in prepare-and-measure scenarios without receiver inputs

TL;DR

This paper systematically analyzes prepare-and-measure quantum scenarios without receiver inputs, revealing how entanglement and measurement strategies enable quantum advantages and their implications for certification experiments.

Contribution

It identifies minimal and next-to-minimal scenarios with quantum advantage, highlighting the role of high-dimensional entanglement and nonlocality, and explores quantum message read-out effects.

Findings

High-dimensional entanglement maximizes quantum advantage.

Nonlocality of CHSH type enables advantages in minimal scenarios.

Non-projective measurements amplify quantum advantages with quantum messages.

Abstract

The most elementary prepare-and-measure scenarios have no independent measurement inputs. No inputs mean that quantum advantages require two indispensable ingredients: shared entanglement and measurements that can be adapted to the communicated messages. Understanding these scenarios is therefore conceptually natural, but also practically relevant, since they act as testbeds for black-box certification of adaptive one-way LOCC. Here, we study them systematically and reveal several of their basic features. For classical messages, we first identify the minimal scenario with a quantum advantage and show that it is maximised by high-dimensional entanglement. Then, we identify the next-to-minimal scenario, and show that quantum advantages can be propelled by nonlocality of the Clauser-Horne-Shimony-Holt type, which makes this an appropriate setting for certification experiments. Proceeding further, we replace classical messages with quantum messages, but require the receiver to read the message before measuring the entangled particle. We show that this leads to amplified quantum advantages, that are made possible only thanks to non-projective message read-out. This in dispensable role of non-projective measurements challenges the common wisdom that they play a secondary role in revealing the power of quantum correlations in black-box experiments.