  In two-dimensional (2D) electron systems under strong magnetic fields,
interactions can cause fractional quantum Hall (FQH) effects. Bringing two 2D
conductors to proximity, a new set of correlated states can emerge due to
interactions between electrons in the same and opposite layers. Here we report
interlayer correlated FQH states in a system of two parallel graphene layers
separated by a thin insulator. Current flow in one layer generates different
quantized Hall signals in the two layers. This result is interpreted by
composite fermion (CF) theory with different intralayer and interlayer
Chern-Simons gauge-field coupling. We observe FQH states corresponding to
integer values of CF Landau level (LL) filling in both layers, as well as
"semi-quantized" states, where a full CF LL couples to a continuously varying
partially filled CF LL. Remarkably, we also recognize a quantized state between
two coupled half-filled CF LLs, attributable to an interlayer CF exciton
condensate.
