  The use of higher-dimensional photonic encodings (qudits) instead of
two-dimensional encodings (qubits) can improve the loss tolerance and reduce
the computational resources of photonic-based quantum information processing.
To harness this potential, efficient schemes for entangling operations such as
the high-dimensional generalization of a linear optics Bell measurement will be
required. We show how an efficient high-dimensional entangled state analyzer
can be implemented with a linear optics interferometer and auxiliary photonic
states. The degree of entanglement of the auxiliary state is much less than in
previous protocols as quantified by an exponentially smaller Schmidt rank. In
addition, the auxiliary state only occupies a single spatial mode, allowing it
to be generated deterministically from a single quantum emitter coupled to a
small qubit register. The reduced complexity of the auxiliary states results in
a high robustness to imperfections and we show that auxiliary states with
fidelities > 0.9 for qudit dimensions 4 can be generated in the presence of
qubit error rates on the order of 10%. This paves the way for experimental
demonstrations with current hardware.
