  We show that correlations inconsistent with any locally causal description
can be a generic feature of measurements on entangled quantum states.
Specifically, spatially-separated parties who perform local measurements on a
maximally-entangled state using randomly chosen measurement bases can, with
significant probability, generate nonclassical correlations that violate a Bell
inequality. For n parties using a Greenberger-Horne-Zeilinger state, this
probability of violation rapidly tends to unity as the number of parties
increases. We also show that, even with both a randomly chosen two-qubit pure
state and randomly chosen measurement bases, a violation can be found about 10%
of the time. Amongst other applications, our work provides a feasible
alternative for the demonstration of Bell inequality violation without a shared
reference frame.
