Optimal Verification of Greenberger-Horne-Zeilinger States

Zihao Li, Yun-Guang Han, and Huangjun Zhu

Phys. Rev. Applied 13, 054002 – Published 1 May 2020

Abstract

We construct optimal protocols for verifying qubit and qudit Greenberger-Horne-Zeilinger (GHZ) states using local projective measurements. When the local dimension is a prime, an optimal protocol is constructed from Pauli measurements only. Our protocols provide a highly efficient way to estimate the fidelity and to certify genuine multipartite entanglement. In particular, they enable the certification of genuine multipartite entanglement using only one test when the local dimension is sufficiently large. By virtue of adaptive local projective measurements, we then construct protocols for verifying GHZ-like states that are optimal over all protocols based on one-way communication. The efficiency can be improved further if additional communications are allowed. Finally, we construct optimal protocols for verifying GHZ states and nearly optimal protocols for GHZ-like states in the adversarial scenario.

Received 22 November 2019
Revised 8 March 2020
Accepted 2 April 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.054002

Physics Subject Headings (PhySH)

Quantum benchmarking Quantum entanglement Quantum information processing Quantum tomography

Quantum Information, Science & Technology

Authors & Affiliations

Zihao Li^1,2, Yun-Guang Han^1,2, and Huangjun Zhu ^1,2,3,4,*

¹Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China
²State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
³Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai 200433, China
⁴Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China