Berlin 2024 – scientific programme

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QI: Fachverband Quanteninformation

QI 24: Verification and Benchmarking of Quantum Systems

QI 24.6: Talk

Thursday, March 21, 2024, 11:00–11:15, HFT-TA 441

Overlapping tomography: Reducing the number of measurement settings — •Kiara Hansenne, Lisa Weinbrenner, Carlos de Gois, and Otfried Gühne — Universität Siegen, Germany

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) log^2(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.

Keywords: Quantum tomography; Marginal problem; Combinatorial designs