Gaussian-state theory of two-photon imaging

Spontaneous parametric downconversion produces entangled signal and idler fields that are in a zero-mean jointly Gaussian state whose postselected, low-brightness, low-flux limit is a biphoton. This paper applies Gaussian-state analysis to two biphoton-state quantum imaging scenarios: far field diffraction-pattern imaging; and broadband thin-lens imaging. It is shown that the spatial resolution behavior in both cases is controlled by the nonzero phase-sensitive cross correlation between the signal and idler fields. Thus, the same resolution can be achieved in these two configurations with classical-state signal and idler fields possessing a nonzero phase-sensitive cross correlation. In other words, the image formation process in these two scenarios is intrinsically classical coherence propagation.