  The NOT gate that flips a classical bit is ubiquitous in classical
information processing. However its quantum analogue, the universal NOT (UNOT)
gate that flips a quantum spin in any alignment into its antipodal counterpart
is strictly forbidden. Here we explore the connection between this discrepancy
and how UNOT gates affect classical and quantum correlations. We show that
while a UNOT gate always preserves classical correlations between two spins, it
can non-locally increase or decrease their shared discord in ways that allow
violation of the data processing inequality. We experimentally illustrate this
using a multi-level trapped \Yb ion that allows simulation of anti-unitary
operations.
