Take the Mach-Zehnder interferometer as an example. A photon passes through a beam splitter, is reflected off mirrors, and interferes with itself at another half-silvered mirror. No measurements or disturbances are made in between. The preferred basis of the photon is given by which path it takes after passing the second beam splitter. The problem is, this preferred basis is nonlocal in between.
Is there a problem with locality here, or is silly ol' me just plain confused?