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Entropy 2013, 15(6), 2340-2362; doi:10.3390/e15062340

Quantum Contextuality with Stabilizer States

Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland
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Received: 1 April 2013 / Revised: 29 May 2013 / Accepted: 1 June 2013 / Published: 7 June 2013
(This article belongs to the Special Issue Quantum Information 2012)
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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.
Keywords: contextuality; stabilizer; non-locality contextuality; stabilizer; non-locality
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Howard, M.; Brennan, E.; Vala, J. Quantum Contextuality with Stabilizer States. Entropy 2013, 15, 2340-2362.

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