Optimal verification and fidelity estimation of maximally entangled states

Zhu, Huangjun1,2,3,4,5; Hayashi, Masahito6,7,8

2019-05-28

10.1103/PhysRevA.99.052346

PHYSICAL REVIEW A   影响因子和分区

2469-9926

2469-9934

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.

SCI ; EI

英语

其他

Japan Society for the Promotion of Science (JSPS)[17H01280] ; Japan Society for the Promotion of Science (JSPS)[16KT0017]

Optics ; Physics

Optics ; Physics, Atomic, Molecular & Chemical

WOS:000469323700009

AMER PHYSICAL SOC

20192307002537

Quantum Theory; Quantum Mechanics:931.4

PHYSICS

Web of Science

1.Fudan Univ, Dept Phys, Shanghai 200433, Peoples R China
2.Fudan Univ, Ctr Field Theory & Particle Phys, Shanghai 200433, Peoples R China
3.Fudan Univ, State Key Lab Surface Phys, Shanghai 200433, Peoples R China
4.Fudan Univ, Inst Nanoelect Devices & Quantum Comp, Shanghai 200433, Peoples R China
5.Collaborat Innovat Ctr Adv Microstruct, Nanjing 210093, Jiangsu, Peoples R China
6.Nagoya Univ, Grad Sch Math, Nagoya, Aichi 4648602, Japan
7.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
8.Natl Univ Singapore, Ctr Quantum Technol, 3 Sci Dr 2, Singapore 117542, Singapore

Zhu, Huangjun,Hayashi, Masahito. Optimal verification and fidelity estimation of maximally entangled states[J]. PHYSICAL REVIEW A,2019,99(5).

Zhu, Huangjun,&Hayashi, Masahito.(2019).Optimal verification and fidelity estimation of maximally entangled states.PHYSICAL REVIEW A,99(5).

Zhu, Huangjun,et al."Optimal verification and fidelity estimation of maximally entangled states".PHYSICAL REVIEW A 99.5(2019).