  A Sagnac loop structure can help overcome the major difficulty in the
practical implementation of a twin field quantum key distribution (TFQKD)
network, namely, the need to stabilize the phase of a quantum state over many
kilometers of fiber. Unfortunately, Rayleigh backscattering noise limits the
signal-to-noise ratio for Sagnac systems containing long fibers and lossy
photonic devices. Here, we solve this problem by sending optical pulses in long
on-off bursts and using time post-selection on measurements taken with free-run
single-photon avalanche detectors. We also investigate the impact of the
residual phase noise uncompensated by the Sagnac structure and find that the
variance of the phase noise scales as loop length to the third power, verifying
an existing calculation in the literature. We measure the interference
visibility in Sagnac loops of varying length without active phase or
polarization stabilization and achieve > 97% visibility in 200 km
ultra-low-loss fiber, which is, to our knowledge, the longest fiber Sagnac
interferometer demonstrated. Our results indicate the suitability of a Sagnac
system for long-distance TFQKD networks, an important step towards the
practical implementation of metropolitan quantum networks.
