  Entangled biphoton sources exhibit nonclassical characteristics and have been
applied to imaging techniques such as ghost imaging, quantum holography, and
quantum optical coherence tomography. The development of wide-field quantum
imaging to date has been hindered by low spatial resolutions, speeds, and
contrast-to-noise ratios (CNRs). Here, we present quantum microscopy by
coincidence (QMC) with balanced pathlengths, which enables super-resolution
imaging at the Heisenberg limit with substantially higher speeds and CNRs than
existing wide-field quantum imaging methods. QMC benefits from a configuration
with balanced pathlengths, where a pair of entangled photons traversing
symmetric paths with balanced optical pathlengths in two arms behave like a
single photon with half the wavelength, leading to 2-fold resolution
improvement. Concurrently, QMC resists stray light up to 155 times stronger
than classical signals. The low intensity and entanglement features of
biphotons in QMC promise nondestructive bioimaging. QMC advances quantum
imaging to the microscopic level with significant improvements in speed and CNR
toward bioimaging of cancer cells. We experimentally and theoretically prove
that the configuration with balanced pathlengths illuminates an avenue for
quantum-enhanced coincidence imaging at the Heisenberg limit.
