We use a path integral quantum Monte Carlo method to simulate excitons and biexcitons in core shell nanocrystals with Type-I, II and quasi-Type II band alignments. Quantum Monte Carlo techniques allow for all quantum correlations to be included when determining the thermal ground state, thus producing accurate predictions of biexciton binding. These subtle quantum correlations are found to cause the biexciton to be binding with Type-I carrier localization and strongly anti-binding with Type-II carrier localization, in agreement with experiment for both core shell nanocrystals and dot in rod nanocrystal structures. Simple treatments based on perturbative approaches are shown to miss this important transition in the biexciton binding. Understanding these correlations offers prospects to engineer strong biexciton anti-binding which is crucial to the design of nanocrystals for single exciton lasing applications.

10 pages, 11 figures