  Quantum sorter has gained a lot of attention during the last years due to its
wide application in quantum information processing and quantum technologies. A
challenging task is the construction of a quantum sorter, which collect many
high-dimensional quantum systems, which are simultaneously incident on
different input ports of the device. In this paper we give the definition of
the general quantum sorter of multi-level quantum systems. We prove the
impossibility of the construction of the perfect quantum sorter, which works
for many particles incident on any input port, while keeping their states
unmodified. Further we propose an approximate multi-particle multi-input-port
quantum sorter, which performs the selection of the particles in a certain
output port according to the properties of the initial states, but changing the
final states. This method is useful for those situations which require high
speed of quantum state sorting. Thus, the information contained in the initial
states of the particles is revealed by the click statistics of the detectors
situated in each output port.
