Contextuality and the Single-Qubit Stabilizer Subtheory

Physical Review Letters
Piers LillystoneJoseph Emerson

Abstract

Contextuality is a fundamental nonclassical property of quantum theory, which has recently been proven to be a key resource for achieving quantum speed-ups in some leading models of quantum computation. However, which of the forms of contextuality, and how much thereof, are required to obtain a speed-up in an arbitrary model of quantum computation remains unclear. In this Letter, we show that the relation between contextuality and a computational advantage is more complicated than previously thought. We achieve this by proving that generalized contextuality is present even within the simplest subset of quantum operations, the so-called single-qubit stabilizer theory, which offers no computational advantage and was previously believed to be completely noncontextual. However, the contextuality of the single-qubit stabilizer theory can be confined to transformations. Therefore, our result also demonstrates that the commonly considered prepare-and-measure scenarios (which ignore transformations) do not fully capture the contextuality of quantum theory.

References

Dec 31, 1990·Physical Review Letters·N D Mermin
Jun 1, 2001·Physical Review Letters·R Raussendorf, H J Briegel
Sep 4, 2008·Physical Review Letters·Robert W Spekkens
Sep 4, 2008·Physical Review Letters·Alexander A KlyachkoAlexander S Shumovsky
Dec 31, 2008·Physical Review Letters·Adán Cabello
Mar 10, 2012·Physical Review Letters·Sixia Yu, C H Oh
Mar 4, 2014·Physical Review Letters·Adán CabelloAndreas Winter
Jun 12, 2014·Nature·Mark HowardJoseph Emerson
Mar 22, 2013·Physical Review Letters·M S Leifer, O J E Maroney
Sep 26, 2015·Physical Review Letters·Ravi Kunjwal, Robert W Spekkens
Jan 18, 2018·Physical Review Letters·Juan Bermejo-VegaRobert Raussendorf
Apr 26, 2018·Physical Review Letters·Adán CabelloZhen-Peng Xu

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Citations

Sep 17, 2019·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Barbara Amaral

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