  The black hole information problem has motivated many proposals for new
physics. One idea, known as state-dependence, is that quantum mechanics must be
generalized to describe the physics of black holes, and that fixed linear
operators do not provide the fundamental description of experiences for
infalling observers. Instead, such experiences are to be described by operators
with an extra dependence on the global quantum state. We show that any
implementation of this idea strong enough to remove firewalls from generic
states requires massive violations of the Born rule. We also demonstrate a
sense in which such violations are visible to infalling observers involved in
preparing the initial state of the black hole. We emphasize the generality of
our results; no details of any specific proposal for state-dependence are
required.
