Kiara Hansenne M.Sc., Universität Siegen

Kiara Hansenne, M.Sc., Universität Siegen

Quantum state tomography aims at reconstructing the density operator of a quantum system using data acquired from measurements on several copies of the system's state. While the conventional approach demands an exponential increase in measurement settings with the growth of particle numbers, certain situations only necessitate access to the density operators of k-body reduced states. Notably, for n-qubit systems, prior studies have shown that the number of Pauli measurement settings scales as e^O(k) log²(n). In this work, we present insights from a one-to-one correspondence with a well-studied problem in combinatorics, and show how to explicitly obtain optimal measurement settings. Furthermore, by dropping the Pauli measurement assumption, we demonstrate the feasibility of marginal tomography with 3^k measurement settings, independently of the number of qubits.