  We find quantum signatures of classical chaos in various metrics of
information gain in quantum tomography. We employ a quantum state estimator
based on weak collective measurements of an ensemble of identically prepared
systems. The tomographic measurement record consists of a sequence of
expectation values of a Hermitian operator that evolves under repeated
application of the Floquet map of the quantum kicked top. We find an increase
in information gain and hence higher fidelities in the reconstruction algorithm
when the chaoticity parameter map increases. The results are well predicted by
random matrix theory.
