Quantifying necessary quantum resources for nonlocality

TL;DR

This paper quantifies the minimal quantum state purity needed to achieve specific Bell inequality violations, linking it to other quantum resources like coherence and entanglement, and revealing nuanced relationships between measurement and state resources.

Contribution

It introduces a method to quantify the minimal purity required for Bell violations, connecting it to various quantum resources and providing new insights into the CHSH inequality.

Findings

Minimal purity determines Bell violation thresholds

Increased measurement resources do not always reduce state resource needs

Quantifies coherence, discord, and entanglement requirements for nonlocality

Abstract

Nonlocality is one of the most important resources for quantum information protocols. The observation of nonlocal correlations in a Bell experiment is the result of appropriately chosen measurements and quantum states. We quantify the minimal purity to achieve a certain Bell value for any Bell operator. Since purity is the most fundamental resource of a quantum state, this enables us also to quantify the necessary coherence, discord, and entanglement for a given violation of two-qubit correlation inequalities. Our results shine new light on the CHSH inequality by showing that for a fixed Bell violation an increase in the measurement resources does not always lead to a decrease of the minimal state resources.