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
* Author to whom correspondence should be addressed.
Received: 1 April 2013; in revised form: 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

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MDPI and ACS Style

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

AMA Style

Howard M, Brennan E, Vala J. Quantum Contextuality with Stabilizer States. Entropy. 2013; 15(6):2340-2362.

Chicago/Turabian Style

Howard, Mark; Brennan, Eoin; Vala, Jiri. 2013. "Quantum Contextuality with Stabilizer States." Entropy 15, no. 6: 2340-2362.

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