Controlled and combined remote implementations of partially unknown quantum operations of multiqubits using GHZ states

摘要

We propose and prove protocols of controlled and combined remoteimplementations of partially unknown quantum operations belonging to therestricted sets [An Min Wang: PRA, \textbf{74}, 032317(2006)] using GHZ states.We detailedly describe the protocols in the cases of one qubit, respectively,with one controller and with two senders. Then we extend the protocols to thecases of multiqubits with many controllers and two senders. Because ourprotocols have to demand the controller(s)'s startup and authorization or twosenders together working and cooperations, the controlled and combined remoteimplementations of quantum operations definitely can enhance the security ofremote quantum information processing and potentially have more applications.Moreover, our protocol with two senders is helpful to farthest arrive at thepower of remote implementations of quantum operations in theory since thedifferent senders perhaps have different operational resources and differentoperational rights in practice.