Entanglement concentration protocols for quantum entangled states

¹ College of Information Science and Technology, Jinan University - Guangzhou 510632, China
² Guangxi Key Laboratory of Cryptography and Information Security - Guilin 541004, China
³ School of Mathematical Science, Heilongjiang University - Harbin 150080, China
⁴ School of Information, Central University of Finance and Economics - Beijing 100081, China

^(a) tingtingsong@jnu.edu.cn (corresponding author)

Received: 21 October 2021
Accepted: 27 January 2022

Abstract

Noise in the channel affects the security of cryptography protocols. The obvious solution for quantum protocols is to estimate the transformation of quantum states caused by the noise. Cluster states are the basic structures of quantum cryptography protocols, which are transmitted through the lossy quantum channel during the procedure of the protocols. The entanglement of the cluster states is extremely fragile and easy to be inflected by inevitable interaction with the environment. To ensure the fidelity of cluster states, the entanglement of the states must be concentrated after the transmission. We propose four protocols to concentrate the entanglement of five-photon linear cluster states by linear optics, in two of which only three parties should perform the local POVM operations. All the protocols reach the maximum of successful probability, and furthermore they are implemented by the linear optics alone. The simulation results depict that lots of five-photon linear cluster states could be concentrated via our protocols, and those protocols are robust against the accuracy of the linear optics. Hence, our protocols are valuable in many fields of quantum information and quantum cryptography.