Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices

摘要

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