Abstract
We propose a deterministic protocol for three distant parties to cooperate so that two parties can implement their secret unitary operators on the third party’s secret quantum state via shared quantum channel assisted by cross-Kerr nonlinearities. The operators are of general form while the state may be encoded either in spatial degree of freedom or polarization degree of freedom. The quantum channel is served by a three-photon hyperentangled state establishing the minimum of consumed photon number for this type of task. This protocol can be named joint remote implementation of operators which is necessary for distributed quantum tasks throughout a quantum network.
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