Holography is a cornerstone characterisation and imaging technique that can be applied to the full electromagnetic spectrum, from X-rays to radio waves or even particles such as neutrons. The key property in all these holographic approaches is coherence that is required to extract the phase information through interference with a reference beam - without this, holography is not possible. Here we introduce a holographic imaging approach that operates on intrinsically incoherent and unpolarised beams, so that no phase information can be extracted from a classical interference measurement. Instead, the holographic information is encoded in the second order coherence of entangled states of light. Using spatial-polarisation hyper-entangled photons pairs, we remotely reconstruct phase images of complex objects. Information is encoded into the polarisation degree of the entangled state, allowing us to image through dynamic phase disorder and even in the presence of strong classical noise, with enhanced spatial resolution compared to classical coherent holographic systems. Beyond imaging, quantum holography quantifies hyper-entanglement distributed over 10^4 modes via a spatially-resolved Clauser-Horne-Shimony-Holt inequality measurement, with applications in quantum state characterisation.
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