A Hierarchy in Majorana Non-Abelian Tests and Hidden Variable Models

doi:10.1088/0256-307X/40/10/100501

Chin. Phys. Lett.

2023, Vol. 40

Issue (10): 100501 DOI: 10.1088/0256-307X/40/10/100501

GENERAL

A Hierarchy in Majorana Non-Abelian Tests and Hidden Variable Models

Peng Qian¹ and Dong E. Liu^2,1,3,4*

¹Beijing Academy of Quantum Information Sciences, Beijing 100193, China
²State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
³Frontier Science Center for Quantum Information, Beijing 100184, China
⁴Hefei National Laboratory, Hefei 230088, China

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Peng Qian and Dong E. Liu 2023 Chin. Phys. Lett. 40 100501

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Abstract The recent progress of the Majorana experiments paves a way for the future tests of non-Abelian braiding statistics and topologically protected quantum information processing. However, a deficient design in those tests could be very dangerous and reach false-positive conclusions. A careful theoretical analysis is necessary so as to develop loophole-free tests. We introduce a series of classical hidden variable models to capture certain key properties of Majorana system: non-locality, topologically non-triviality, and quantum interference. Those models could help us to classify the Majorana properties and to set up the boundaries and limitations of Majorana non-Abelian tests: fusion tests, braiding tests and test set with joint measurements. We find a hierarchy among those Majorana tests with increasing experimental complexity.

Received: 02 July 2023 Editors' Suggestion Published: 22 September 2023

PACS:	05.30.Pr	(Fractional statistics systems)
	03.65.-w	(Quantum mechanics)
	03.65.Ta	(Foundations of quantum mechanics; measurement theory)

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	Peng Qian and Dong E. Liu

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