Optimal verification and fidelity estimation of maximally entangled states

Huangjun Zhu and Masahito Hayashi
Phys. Rev. A 99, 052346 – Published 28 May 2019

Abstract

We study the verification of maximally entangled states by virtue of the simplest measurement settings: local projective measurements without adaption. We show that optimal protocols are in one-to-one correspondence with complex projective 2-designs constructed from orthonormal bases. Optimal protocols with minimal measurement settings are in one-to-one correspondence with complete sets of mutually unbiased bases. Based on this observation, optimal protocols are constructed explicitly for any local dimension, which can also be applied to estimating the fidelity with the target state and to detecting entanglement. In addition, we show that incomplete sets of mutually unbiased bases are optimal for verifying maximally entangled states when the number of measurement settings is restricted. Moreover, we construct optimal protocols for the adversarial scenario in which state preparation is not trusted. The number of tests has the same scaling behavior as the counterpart for the nonadversarial scenario; the overhead is no more than three times. We also show that the entanglement of the maximally entangled state can be certified with any given significance level using only one test as long as the local dimension is large enough.

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  • Received 20 February 2019

DOI:https://doi.org/10.1103/PhysRevA.99.052346

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Huangjun Zhu1,2,3,4,* and Masahito Hayashi5,6,7,†

  • 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
  • 5Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan
  • 6Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
  • 7Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117542 Singapore

  • *zhuhuangjun@fudan.edu.cn
  • masahito@math.nagoya-u.ac.jp

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Issue

Vol. 99, Iss. 5 — May 2019

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