  In this study, we explore the theoretical application of entangled multi-mode
squeezed light for label-free optical super-resolution imaging. By generating
massively entangled multi-mode squeezed light through an array of balanced beam
splitters, using a single-mode squeezed light input, we create a multi-mode
quantum light state with exceptional entanglement and noise suppression below
the shot noise level. This significantly reduces imaging measurement errors
compared to classical coherent state light imaging when the same number of
photons are used on the imaging sample. We demonstrate how to optimize the
imaging system's parameters to achieve the Heisenberg imaging error limit,
taking into account the number of entangled modes and photons used. We also
examine the effects of optical losses in the imaging system, necessitating
adjustments to the optimized parameters based on the degree of optical loss. In
practical applications, this new quantum imaging approach reduces the number of
photons needed to achieve the same image quality by two orders of magnitude
compared to classical imaging methods that use non-entangled, non-squeezed
coherent state light.
