  Homodyne X-ray diffraction signals produced by classical light and classical
detectors are given by the modulus square of the charge density in momentum
space $\left|\sigma(\mathbf{q})\right|^{2}$, missing its phase which is
required in order to invert the signal to real space. We show that quantum
detection of the radiation field yields a linear diffraction pattern that
reveals $\sigma(\mathbf{q})$ itself, including the phase. We further show that
repeated diffraction measurements with variable delays constitute a novel
multidimensional measure of spontaneous charge-density fluctuations. Classical
diffraction, in contrast, only reveals a subclass of even-order correlation
functions. Simulations of two dimensional signals obtained by two diffraction
events are presented for the amino acid cysteine.
