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High-dimensional entangled states are of significant interest in quantumscience as they increase the information content per photon and can remainentangled in the presence of significant noise. We develop the analyticaltheory and show experimentally that the noise tolerance of high-dimensionalentanglement can be significantly increased by modest increases to the size ofthe Hilbert space. For example, doubling the size of a Hilbert space with localdimension d=300 leads to a reduction of the threshold detector efficienciesrequired for entanglement certification by two orders of magnitude. This workis developed in the context of spatial entanglement, but it can easily betranslated to photonic states entangled in different degrees of freedom. Wealso demonstrate that knowledge of a single parameter, the signal-to-noiseratio, precisely links measures of entanglement to a range of experimentalparameters quantifying noise in a quantum communication system, enablingaccurate predictions of its performance. This work serves to answer a simplequestion: "Is high-dimensional photonic entaglement robust to noise?". Here weshow that the answer is more nuanced than a simple "yes" or "no" and involves acomplex interplay between the noise characteristics of the state, channel, anddetection system

Is high-dimensional photonic entanglement robust to noise?