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High-dimensional entangled states are of significant interest in quantum science as they increase the information content per photon and can remain entangled in the presence of significant noise. We develop the analytical theory and show experimentally that the noise tolerance of high-dimensional entanglement can be significantly increased by modest increases to the size of the Hilbert space. For example, doubling the size of a Hilbert space with local dimension d=300 leads to a reduction of the threshold detector efficiencies required for entanglement certification by two orders of magnitude. This work is developed in the context of spatial entanglement, but it can easily be translated to photonic states entangled in different degrees of freedom. We also demonstrate that knowledge of a single parameter, the signal-to-noise ratio, precisely links measures of entanglement to a range of experimental parameters quantifying noise in a quantum communication system, enabling accurate predictions of its performance. This work serves to answer a simple question: Is high-dimensional photonic entaglement robust to noise?. Here we show that the answer is more nuanced than a simple yes or no and involves a complex interplay between the noise characteristics of the state, channel, and detection system
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