Berlin 2024 – wissenschaftliches Programm

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QI: Fachverband Quanteninformation

QI 24: Verification and Benchmarking of Quantum Systems

QI 24.11: Vortrag

Donnerstag, 21. März 2024, 12:30–12:45, HFT-TA 441

User-friendly confidence regions for quantum state tomography — •Carlos de Gois and Matthias Kleinmann — Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany

Quantum state tomography is the standard technique for reconstructing a quantum state from measurement data. In practice, only a finite number of copies of the unknown state can be measured, thus the estimated state will almost surely diverge from the true state. A common way to express this limited knowledge about the true state is by providing confidence regions that contain the true state with high probability. Although some methods to construct such confidence regions already exist, they all have drawbacks such as requiring too many samples, not generalizing to arbitrary measurements, or being difficult to describe. In this talk, I will discuss a new construction that overcomes these issues. The resulting regions are described by ellipsoids in the space of Hermitian operators, have an asymptotically optimal sample cost, and can be straightforwardly applied to any measurement scheme. To investigate their performance in practice, I will use simulated tomography experiments to compare the sample costs with respect to previous proposals, and show that our construction leads to tighter regions, especially for high-dimensional systems.

Keywords: quantum tomography; confidence regions