  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.
