  The Bell basis is a distinctive set of maximally entangled two-particle
quantum states that forms the foundation for many quantum protocols such as
teleportation, dense coding and entanglement swapping. While the generation,
manipulation, and measurement of two-level quantum states is well understood,
the same is not true in higher dimensions. Here we present the experimental
generation of a complete set of Bell states in a four-dimensional Hilbert
space, comprising of 16 orthogonal entangled Bell-like states encoded in the
orbital angular momentum of photons. The states are created by the application
of generalized high-dimensional Pauli gates on an initial entangled state. Our
results pave the way for the application of high-dimensional quantum states in
complex quantum protocols such as quantum dense coding.
