  The Born rule, a foundational axiom used to deduce probabilities of events
from wavefunctions, is indispensable in the everyday practice of quantum
physics. It is also key in the quest to reconcile the ostensibly inconsistent
laws of the quantum and classical realms, as it confers physical significance
to reduced density matrices, the essential tools of decoherence theory.
Following Bohr's Copenhagen interpretation, textbooks postulate the Born rule
outright. However, recent attempts to derive it from other quantum principles
have been successful, holding promise for simplifying and clarifying the
quantum foundational bedrock. A major family of derivations is based on
envariance, a recently discovered symmetry of entangled quantum states. Here,
we identify and experimentally test three premises central to these
envariance-based derivations, thus demonstrating, in the microworld, the
symmetries from which the Born rule is derived. Further, we demonstrate
envariance in a purely local quantum system, showing its independence from
relativistic causality.
