  With the Deep Underground Neutrino Experiment (DUNE) as an example, we show
that the presence of even one sterile neutrino of mass $\sim$1 eV can
significantly impact the measurements of CP violation in long baseline
experiments. Using a probability level analysis and neutrino-antineutrino
asymmetry calculations, we discuss the large magnitude of these effects, and
show how they translate into significant event rate deviations at DUNE. Our
results demonstrate that measurements which, when interpreted in the context of
the standard three family paradigm, indicate CP conservation at long baselines,
may, in fact hide large CP violation if there is a sterile state. Similarly,
any data indicating the violation of CP cannot be properly interpreted within
the standard paradigm unless the presence of sterile states of mass O(1 eV) can
be conclusively ruled out. Our work underscores the need for a parallel and
linked short baseline oscillation program and a highly capable near detector
for DUNE, in order that its highly anticipated results on CP violation in the
lepton sector may be correctly interpreted.
