An illustrative downhole sensing system includes a phase-squeezer assembly, an interferometer with a downhole sensor on the sensing path, and a receiver. The phase squeezer assembly provides a phase-squeezed laser beam, preferably with a squeeze parameter greater than 2. Certain embodiments include a pulse generator that gates the phase-squeezed laser beam to form a sequence of phase-squeezed laser pulses, and may further include a compensator that converts the sequence of pulses into a sequence of double pulses with a slight frequency shift between the pulses in each pair. The interferometer conveys a reference portion of the phase-squeezed laser beam along a reference path and a sensing portion of the phase-squeezed laser beam along a sensing path. A downhole sensor along the sensing path provides the sensing portion of the phase-squeezed laser beam with a measurement-parameter dependent phase shift relative to the reference portion of the phase-squeezed laser beam, which is measured by the receiver.