  Lattice QCD simulations of multi-baryon correlation functions can predict the
structure and reactions of nuclei without encountering the baryon chemical
potential sign problem. However, they suffer from a signal-to-noise problem
where Monte Carlo estimates of observables have quantum fluctuations that are
exponentially larger than their average values. Recent lattice QCD results
demonstrate that the complex phase of baryon correlations functions relates the
baryon signal-to-noise problem to a sign problem and exhibits unexpected
statistical behavior resembling a heavy-tailed random walk on the unit circle.
Estimators based on differences of correlation function phases evaluated at
different Euclidean times are discussed that avoid the usual signal-to-noise
problem, instead facing a signal-to-noise problem as the time interval
associated with the phase difference is increased, and allow hadronic
observables to be determined from arbitrarily large-time correlation functions.
