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Measuring the state of a quantum system is a fundamental process in quantummechanics and plays an essential role in quantum information and quantumtechnologies. One method to measure a quantum observable is to sort the systemin different spatial modes according to the measured value, followed bysingle-particle detectors on each mode. Examples of quantum sorters arepolarizing beam-splitters (PBS) -- which direct photons according to theirpolarization -- and Stern-Gerlach devices. Here we propose a general scheme tosort a quantum system according to the value of any $d$-dimensional degree offreedom, such as spin, orbital angular momentum (OAM), wavelength etc. Ourscheme is universal, works at the single-particle level and has a theoreticalefficiency of 100\%. As an application we design an efficient OAM sorterconsisting of a single multi-path interferometer which is suitable for aphotonic chip implementation.

Sorting quantum systems efficiently