but in different other relevant orthogonal bases. Specifically, in the time-bin basis and a basis obtained by a Schmidt decomposition. Moreover, we show that the presented method is well suited to gain physical insights, e.g. with respect to the coherence time of the entangled photons in the time-bin basis. The projection onto Schmidt modes further lays the groundwork for a reconstruction of the SPDC state in terms of the Schmidt basis in the frequency domain.

The paper is organized as follows: In section 2 we introduce the general theoretical framework to discretize a continuous frequency space in a countable subspace together with three specific realizations: Frequency bins, time bins and Schmidt modes. Subsequently, we describe the experimental setup in section 3. In section 4, we experimentally demonstrate and quantify entanglement in the three bases by means of projective measurements equivalent to two-photon interferometry [@franson1989] in the time-bin case. Entangled qudits up to $d=4$ are analyzed within the context of a $d$-dimensional Bell inequality. Finally, we conclude this paper by discussing the limitations of the current setup and the possible improvements in view of higher dimensions.

Theory
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Theoretical framework
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In the following, the theoretical framework of the experimental results 