  The existing notion of the shared entangled state-assisted remote preparation
of unitary operator (equivalently the existing notion of quantum remote
control) using local operation and classical communication is generalized to a
scenario where under the control of a supervisor two users can jointly
implement arbitrary unitaries (one unknown unitary operation by each or
equivalently a single unitary decomposed into two unitaries of the same
dimension and given to two users) on an unknown quantum state available with a
geographically separated user. It is explicitly shown that the task can be
performed using a four-qubit hyperentangled state, which is entangled
simultaneously in both spatial and polarization degrees of freedom of photons.
The proposed protocol which can be viewed as primitive for distributed photonic
quantum computing is further generalized to the case that drops the
restrictions on the number of controllers and the number of parties performing
unitaries and allows both the numbers to be arbitrary. It is also shown that
all the existing variants of quantum remote control schemes can be obtained as
special cases of the present scheme.
