  Quantum nonlocality can be revealed "via local contextuality" in qudit-qudit
entangled systems with $d > 2$, that is, through the violation of inequalities
containing Alice-Bob correlations that admit a local description, and
Alice-Alice correlations (between the results of sequences of measurements on
Alice's subsystem) that admit a local (but contextual) description. A
fundamental question to understand the respective roles of entanglement and
local contextuality is whether nonlocality via local contextuality exists when
the parties have only qubit-qubit entanglement. Here we respond affirmatively
to this question. This result further clarifies the connection between
contextuality and nonlocality and opens the door for observing nonlocality via
local contextuality in actual experiments.
