Quantum Contextuality with Stabilizer States

Entropy

Mark Howard¹  Eoin Brennan² 

[1] Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland;

关键词: contextuality;    stabilizer;    non-locality;   

DOI  :  10.3390/e15062340

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.