  While quantum state tomography plays a vital role in the verification and
benchmarking of quantum systems, it is an intractable task if the
controllability and measurement of quantum registers are constrained. In this
paper, we study the quantum state tomography of star-topology registers, in
which the individual addressability of peripheral spins is infeasible. Based on
the star-symmetry, we decompose the Hilbert space to alleviate the complexity
of tomography and design a compact strategy with minimum number of
measurements. By optimizing the parameterized quantum circuit for information
transfer, the robustness against measurement errors is also improved.
Furthermore, we apply this method to a 10-spin star-topology register and
demonstrate its ability to characterize large-scale systems. Our results can
help future investigations of quantum systems with constrained ability of
quantum control and measurement.
