Quantum Contextuality with Stabilizer States

TL;DR

This paper explores quantum contextuality in stabilizer states, demonstrating how certain state-dependent contextuality phenomena generalize from qubits to higher-dimensional qudits using graph-theoretical methods.

Contribution

It applies a graph-theoretical formalism to stabilizer states, showing the generalization of state-dependent contextuality from qubits to qudits, and analyzes structural properties of stabilizer states.

Findings

State-independent contextuality does not generalize to qudits.

State-dependent contextuality associated with Bell inequalities does generalize.

Structural properties of stabilizer states related to orthogonality are identified.

Abstract

The Pauli groups are ubiquitous in quantum information theory because of their usefulness in describing quantum states and operations and their readily understood symmetry properties. In addition, the most well-understood quantum error correcting codes -- stabilizer codes -- are built using Pauli operators. The eigenstates of these operators -- stabilizer states -- display a structure (e.g., mutual orthogonality relationships) that has made them useful in examples of multi-qubit non-locality and contextuality. Here, we apply the graph-theoretical contextuality formalism of Cabello, Severini and Winter to sets of stabilizer states, with particular attention to the effect of generalizing two-level qubit systems to odd prime d-level qudit systems. While state-independent contextuality using two-qubit states does not generalize to qudits, we show explicitly how state-dependent contextuality associated with a Bell inequality does generalize. Along the way we note various structural properties of stabilizer states, with respect to their orthogonality relationships, which may be of independent interest.