  From correlations in measurement outcomes alone, can two otherwise isolated
parties establish whether such correlations are atemporal? That is, can they
rule out that they have been given the same system at two different times?
Classical statistics says no, yet quantum theory disagrees. Here, we introduce
the necessary and sufficient conditions by which such quantum correlations can
be identified as atemporal. We demonstrate the asymmetry of atemporality under
time reversal, and reveal it to be a measure of spatial quantum correlation
distinct from entanglement. Our results indicate that certain quantum
correlations possess an intrinsic arrow of time, and enable classification of
general quantum correlations across space-time based on their (in)compatibility
with various underlying causal structures.
