TL;DR
This paper explores the relationship between Freudenthal ranks of three-qubit states and their effectiveness in non-local games, revealing a strict hierarchy based on the rank.
Contribution
It establishes a novel connection between Freudenthal ranks and quantum non-local game success rates, providing a new classification framework for three-qubit states.
Findings
Success rates are strictly ordered by Freudenthal rank.
Freudenthal rank provides a hierarchy for three-qubit entanglement.
The classification aids in understanding quantum non-locality.
Abstract
The Hilbert space of three-qubit pure states may be identified with a Freudenthal triple system. Every state has an unique \emph{Freudenthal rank} ranging from 1 to 4, which is determined by a set of automorphism group covariants. It is shown here that the optimal success rates for winning a three-player non-local game, varying over all local strategies, are strictly ordered by the Freudenthal rank of the shared three-qubit resource.
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