The Simplest Demonstrations of Quantum Nonlocality

TL;DR

This paper explores the minimal complexity required to demonstrate quantum nonlocality phenomena like Bell violations, EPR-steering, and entanglement, revealing a hierarchy and proposing simplified measurement strategies that are robust and alignment-free.

Contribution

It introduces a hierarchy of complexity costs for demonstrating quantum correlations and derives minimal measurement schemes using circular 2-designs, including alignment-free photonic demonstrations.

Findings

Bell violation tests are simplest with CHSH inequality.

EPR-steering and entanglement tests can be minimized with non-projective measurements.

Photonic experiments show correlation independence from polarizer angles.

Abstract

We investigate the complexity cost of demonstrating the key types of nonclassical correlations --- Bell inequality violation, EPR-steering, and entanglement --- with independent agents, theoretically and in a photonic experiment. We show that the complexity cost exhibits a hierarchy among these three tasks, mirroring the recently-discovered hierarchy for how robust they are to noise. For Bell inequality violations, the simplest test is the well-known CHSH test, but for EPR-steering and entanglement the tests that involve the fewest number of detection patterns require non-projective measurements. The simplest EPR-steering requires a choice of projective measurement for one agent and a single non-projective measurement for the other, while the simplest entanglement test uses just a single non-projective measurement for each agent. In both of these cases, we derive our inequalities using the concept of circular 2-designs. This leads to the interesting feature that in our photonic demonstrations, the correlation of interest is independent of the angle between the linear polarizers used by the two parties, which thus require no alignment.