The quest for the realization of effective quantum state discrimination
strategies is of great interest for quantum information technology, as well as
for fundamental studies. Therefore, it is crucial to develop new and more
efficient methods to implement discrimination protocols for quantum states.
Among the others, single photon implementations are more advisable, because of
their inherent security advantage in quantum communication scenarios. In this
work, we present the experimental realization of a protocol employing a
time-multiplexing strategy to optimally discriminate among eight non-orthogonal
states, encoded in the four-dimensional Hilbert space spanning both the
polarization degree of freedom and photon energy. The experiment, built on a
custom-designed bulk optics analyser setup and single photons generated by a
nearly deterministic solid-state source, represents a benchmarking example of
minimum error discrimination with actual quantum states, requiring only linear
optics and two photodetectors to be realized. Our work paves the way for more
complex applications and delivers a novel approach towards high-dimensional
quantum encoding and decoding operations