  The photoluminescence intermittency (blinking) of quantum dots is interesting
because it is an easily-measured quantum process whose transition statistics
cannot be explained by Fermi's Golden Rule. Commonly, the transition statistics
are power-law distributed, implying that quantum dots possess at least trivial
memories. By investigating the temporal correlations in the blinking data, we
demonstrate with high statistical confidence that quantum dot blinking data has
non-trivial memory, which we define to be statistical complexity greater than
one. We show that this memory cannot be discovered using the transition
distribution. We show by simulation that this memory does not arise from
standard data manipulations. Finally, we conclude that at least three physical
mechanisms can explain the measured non-trivial memory: 1) Storage of state
information in the chemical structure of a quantum dot; 2) The existence of
more than two intensity levels in a quantum dot; and 3) The overlap in the
intensity distributions of the quantum dot states, which arises from
fundamental photon statistics.
