Controlled remote implementation of operators via hyperentanglement
Nguyen Ba An, Bich Thi Cao
Abstract
Abstract Distributed quantum computation is a good solution for salable quantum computation within a quantum network each node of which just contains reasonably a few number of qubits. Controlled implementation of operators on states of a remote node is thus necessary. In this paper we propose protocols for three kinds of tasks of controlled implementation of operators on remote photon states via one hyperentangled Greenberger–Horne–Zeilinger state assisted with cross-Kerr nonlinearities: one with general operators and photon states in spatial degree of freedom (DOF), another one also with general operators but the photon state being in polarization DOF and the third one with a limited subset of operators acting on photon state in both spatial and polarization degrees of freedom. All the protocols are deterministic and performed in two steps under quantum control in each step.