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

TLDR

Reliable, efficient quantum state determination is essential for quantum information processing, and symmetric informationally complete POVMs provide an unbiased estimator with the minimal number of outcomes, but realizing them requires non‑trivial couplings that can be achieved via Naimark dilation. We propose an experimental design that directly implements SIC‑POVMs on path‑encoded qubits and qutrits using multiport devices, building on recent demonstrations by several groups. The design employs an integrated photonic system of nested linear optical elements to realize the required multiports in practice.

Abstract

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.