Contextuality as a Precondition for Quantum Entanglement

TL;DR

This paper establishes a fundamental link between quantum contextuality and entanglement, showing that entanglement requires contextuality and vice versa, enabling new ways to test and detect these quantum resources.

Contribution

It proves that entanglement can only exist if there is underlying contextuality, connecting nonlocal and sequential quantum scenarios and enabling new tests for quantum resources.

Findings

Entanglement arises only with preparation and measurement contextuality.

Absence of entanglement implies absence of contextuality.

Inequalities for contextuality can be used as entanglement tests.

Abstract

Quantum theory features several phenomena which can be considered as resources for information processing tasks. Some of these effects, such as entanglement, arise in a nonlocal scenario, where a quantum state is distributed between different parties. Other phenomena, such as contextuality, can be observed if quantum states are prepared and then subjected to sequences of measurements. We use robust remote state preparation to connect the nonlocal and sequential scenarios and provide an intimate connection between different resources: We prove that entanglement in a nonlocal scenario can arise only if there is preparation and measurement contextuality in the corresponding sequential scenario and that the absence of entanglement implies the absence of contextuality. As a direct consequence, our result allows us to translate any inequality for testing preparation and measurement contextuality into an entanglement test; in addition, entanglement witnesses can be used to design novel contextuality inequalities.