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Heimendahl, Arne ORCID: 0000-0002-8366-953X, Heinrich, Markus and Gross, David (2022). The axiomatic and the operational approaches to resource theories of magic do not coincide. J. Math. Phys., 63 (11). MELVILLE: AIP Publishing. ISSN 1089-7658

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Abstract

Stabiliser operations occupy a prominent role in fault-tolerant quantum computing. They are defined operationally: by the use of Clifford gates, Pauli measurements and classical control. These operations can be efficiently simulated on a classical computer, a result which is known as the Gottesman-Knill theorem. However, an additional supply of magic states is enough to promote them to a universal, fault-tolerant model for quantum computing. To quantify the needed resources in terms of magic states, a resource theory of magic has been developed. Stabiliser operations (SO) are considered free within this theory, however they are not the most general class of free operations. From an axiomatic point of view, these are the completely stabiliser-preserving (CSP) channels, defined as those that preserve the convex hull of stabiliser states. It has been an open problem to decide whether these two definitions lead to the same class of operations. In this work, we answer this question in the negative, by constructing an explicit counter-example. This indicates that recently proposed stabiliser-based simulation techniques of CSP maps are strictly more powerful than Gottesman-Knill-like methods. The result is analogous to a well-known fact in entanglement theory, namely that there is a gap between the operationally defined class of local operations and classical communication (LOCC) and the axiomatically defined class of separable channels. Published under an exclusive license by AIP Publishing.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Heimendahl, Arne UNSPECIFIED orcid.org/0000-0002-8366-953X UNSPECIFIED Heinrich, Markus UNSPECIFIED UNSPECIFIED UNSPECIFIED Gross, David UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-667061
DOI:	10.1063/5.0085774
Journal or Publication Title:	J. Math. Phys.
Volume:	63
Number:	11
Date:	2022
Publisher:	AIP Publishing
Place of Publication:	MELVILLE
ISSN:	1089-7658
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66706