Optimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks

Abstract Bipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untruste...

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Autores principales:	Yun-Guang Han, Zihao Li, Yukun Wang, Huangjun Zhu
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/4831bea7302e42dba1695d3914c909df
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spelling	oai:doaj.org-article:4831bea7302e42dba1695d3914c909df2021-11-28T12:13:53ZOptimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks10.1038/s41534-021-00499-82056-6387https://doaj.org/article/4831bea7302e42dba1695d3914c909df2021-11-01T00:00:00Zhttps://doi.org/10.1038/s41534-021-00499-8https://doaj.org/toc/2056-6387Abstract Bipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untrusted network in which one party is not honest. Only local projective measurements are required for the honest party. It turns out each verification protocol is tied to a probability distribution on the Bloch sphere and its performance has an intuitive geometric meaning. This geometric picture enables us to construct the optimal and simplest verification protocols, which are also very useful to detecting entanglement in the untrusted network. Moreover, we show that our verification protocols can achieve almost the same sample efficiencies as protocols tailored to standard quantum state verification. Furthermore, we establish an intimate connection between the verification of Greenberger–Horne–Zeilinger states and the verification of the Bell state. By virtue of this connection we construct the optimal protocol for verifying Greenberger–Horne–Zeilinger states and for detecting genuine multipartite entanglement.Yun-Guang HanZihao LiYukun WangHuangjun ZhuNature PortfolioarticlePhysicsQC1-999Electronic computers. Computer scienceQA75.5-76.95ENnpj Quantum Information, Vol 7, Iss 1, Pp 1-7 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95
spellingShingle	Physics QC1-999 Electronic computers. Computer science QA75.5-76.95 Yun-Guang Han Zihao Li Yukun Wang Huangjun Zhu Optimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks
description	Abstract Bipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untrusted network in which one party is not honest. Only local projective measurements are required for the honest party. It turns out each verification protocol is tied to a probability distribution on the Bloch sphere and its performance has an intuitive geometric meaning. This geometric picture enables us to construct the optimal and simplest verification protocols, which are also very useful to detecting entanglement in the untrusted network. Moreover, we show that our verification protocols can achieve almost the same sample efficiencies as protocols tailored to standard quantum state verification. Furthermore, we establish an intimate connection between the verification of Greenberger–Horne–Zeilinger states and the verification of the Bell state. By virtue of this connection we construct the optimal protocol for verifying Greenberger–Horne–Zeilinger states and for detecting genuine multipartite entanglement.
format	article
author	Yun-Guang Han Zihao Li Yukun Wang Huangjun Zhu
author_facet	Yun-Guang Han Zihao Li Yukun Wang Huangjun Zhu
author_sort	Yun-Guang Han
title	Optimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks
title_short	Optimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks
title_full	Optimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks
title_fullStr	Optimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks
title_full_unstemmed	Optimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks
title_sort	optimal verification of the bell state and greenberger–horne–zeilinger states in untrusted quantum networks
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/4831bea7302e42dba1695d3914c909df
work_keys_str_mv	AT yunguanghan optimalverificationofthebellstateandgreenbergerhornezeilingerstatesinuntrustedquantumnetworks AT zihaoli optimalverificationofthebellstateandgreenbergerhornezeilingerstatesinuntrustedquantumnetworks AT yukunwang optimalverificationofthebellstateandgreenbergerhornezeilingerstatesinuntrustedquantumnetworks AT huangjunzhu optimalverificationofthebellstateandgreenbergerhornezeilingerstatesinuntrustedquantumnetworks
_version_	1718408137041510400

Optimal verification of the Bell state and Greenberger–Horne–Zeilinger states in untrusted quantum networks

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