  Upon entangling a spatial binary alternative of a photon with its
polarization, one can use single photons to study arbitrary 2-qubit states.
Sending the photon through a Mach-Zehnder interferometer, equipped with sets of
wave plates that change the polarization, amounts to performing a unitary
transformation on the 2-qubit state. We show that any desired unitary gate can
be realized by a judicious choice of the parameters of the set-up and discuss a
number of applications. They include the diagnosis of an unknown 2-qubit state,
an optical Grover search, and the realization of a thought experiment invented
by Vaidman, Aharonov, and Albert.
