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We propose a method for preparing mixed quantum states of arbitrary dimension$D$ ($D\geq2$) which are codified in the discretized transverse momentum andposition of single photons, once they are sent through an aperture with $D$slits. Following our previous technique we use a programmable single phase-onlyspatial light modulator (SLM) to define the aperture and set the complextransmission amplitude of each slit, allowing the independent control of thecomplex coefficients that define the quantum state. Since these SLMs give usthe possibility to dynamically varying the complex coefficients of the stateduring the measurement time, we can generate not only pure states but alsoquantum states compatible with a mixture of pure quantum states. Therefore, byusing these apertures varying on time according to a probability distribution,we have experimentally obtained $D$-dimensional quantum states with puritiesthat depend on the parameters of the distribution through a clear analyticalexpression. This fact allows us to easily customize the states to be generated.Moreover, the method offer the possibility of working without changing theoptical setup between pure and mixed states, or when the dimensionality of thestates is increased. The obtained results show a quite good performance of ourmethod at least up to dimension $D=11$, being the fidelity of the preparedstates $F > 0.98$ in every case.

Controlled generation of mixed spatial qudits with arbitrary degree of purity