Efficient and robust detection of multipartite Greenberger-Horne-Zeilinger-like states

Qi Zhao, Gerui Wang, Xiao Yuan, and Xiongfeng Ma
Phys. Rev. A 99, 052349 – Published 28 May 2019

Abstract

Entanglement is a key resource for quantum information processing. A widely used tool for detecting entanglement is the entanglement witness, where the measurement of the witness operator is guaranteed to be positive for all separable states and can be negative for certain entangled states. In reality, due to exponentially increasing the Hilbert-space dimension with respect to the system size, it is very challenging to construct an efficient entanglement witness for general multipartite entangled states. For N-partite Greenberger-Horne-Zeilinger (GHZ)-like states, the most robust witness scheme requires N+1 local measurement settings and can tolerate up to 1/2 white noise. As a comparison, the most efficient witness for GHZ-like states only needs two local measurement settings and can tolerate up to 1/3 white noise. There is a tradeoff between the realization efficiency, the number of measurement settings, and the detection robustness, the maximally tolerable white noise. In this paper, we study this tradeoff by proposing a family of entanglement witnesses with k (2kN+1) local measurement settings. Considering symmetric local measurements, we calculate the maximal tolerable noise for any given number of measurement settings. Consequently, we design the optimal witness with a minimal number of settings for any given level of white noise. Our theoretical analysis can be applied to other multipartite entangled states with a strong symmetry. Our witnesses can be easily implemented in experiment and applied in practical multipartite entanglement detection under different noise conditions.

  • Figure
  • Received 22 February 2019

DOI:https://doi.org/10.1103/PhysRevA.99.052349

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Qi Zhao1, Gerui Wang2, Xiao Yuan3,*, and Xiongfeng Ma1,†

  • 1Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
  • 2Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
  • 3Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, England, United Kingdom

  • *xiao.yuan.ph@gmail.com
  • xma@tsinghua.edu.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 99, Iss. 5 — May 2019

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×