Dresden 2026 – scientific programme

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QI: Fachverband Quanteninformation

QI 10: Quantum Information: Concepts and Methods I

QI 10.7: Talk

Wednesday, March 11, 2026, 11:30–11:45, BEY/0137

Entanglement quantification with randomized measurements is maximally difficult — Julian Eisfeld and •Nikolai Wyderka — Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany

The certification of quantum systems is essential for emerging quantum technologies, particularly in quantum communication, networks, and distributed computing, where maintaining a common reference frame across distant nodes poses significant challenges. Reference frame independent approaches, such as randomized measurement schemes, offer a promising route by reducing experimental demands while granting access to basis-independent quantities, including entanglement. However, the efficiency of such schemes in measuring local invariants has remained unclear.

In this contribution, we determine the minimal number of measurement settings required to access all two-qubit invariants using randomized measurement schemes. We further demonstrate that entanglement certification necessarily involves the most demanding invariants, establishing it as a maximally difficult task. Our results reveal a fundamental hierarchy among invariants, with direct implications for experimental feasibility and theoretical understanding of quantum certification. Finally, we extend our analysis beyond bipartite systems by applying it to the Kempe invariant in three-qubit systems, providing a first step toward uncovering similar hierarchies in higher dimensions.

Keywords: Randomized measurements; Local invariants; Observables; Entanglement