  It is crucial for various quantum information processing tasks that the state
of a quantum system can be determined reliably and efficiently from general
quantum measurements. One important class of measurements for this purpose is
symmetric informationally complete positive operator-valued measurements
(SIC-POVMs). SIC-POVMs have the advantage of providing an unbiased estimator
for the quantum state with the minimal number of outcomes needed for full
tomography. By virtue of Naimark's dilation theorem, any POVM can always be
realized with a suitable coupling between the system and an auxiliary system
and by performing a projective measurement on the joint system. In practice,
finding the appropriate coupling is rather non-trivial. Here we propose an
experimental design for directly implementing SIC-POVMs using multiport devices
and path-encoded qubits and qutrits, the utility of which has recently been
demonstrated by several experimental groups around the world. Furthermore, we
describe how these multiports can be attained in practice with an integrated
photonic system composed of nested linear optical elements.
