Entanglement concentration for polarization–spatial–time-bin hyperentangled Bell states

¹ College of Physics Science and Information Engineering, Hebei Advanced Thin Films Laboratory, Hebei Normal University - Shijiazhuang 050024, China
² College of Mathematics and Information Science, Hebei Normal University - Shijiazhuang 050024, China

^(a) flyan@mail.hebtu.edu.cn
^(b) gaoting@mail.hebtu.edu.cn

Received: 2 August 2018
Accepted: 17 September 2018

Abstract

We present two hyperentangled concentration schemes for two-photon systems in a partially hyperentangled Bell state that is simultaneously entangled in polarization, spatial mode and time-bin degrees of freedom (DOFs). The first scheme extracts a maximally hyperentangled Bell state using cross-Kerr nonlinearity, which is discussed in two cases of unknown and known coefficients. We construct quantum nondemolition detectors based on cross-Kerr nonlinearities to implement the polarization and spatial parity check. In this scheme, we only require a small phase shift, as long as it can be distinguished from zero. The second scheme is used to concentrate an initial partially hyperentangled state with only linear optical elements, where coefficients of the initial state are known. Both of the two schemes are feasible with the current experimental technology. Moreover, hyperentanglement DOFs can largely improve the channel capacity of long-distance quantum communication. All of these make our schemes more practical and useful in quantum communication.