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THU: Thursday Contributed Sessions
THU 2: Quantum Information: Concepts and Methods I
THU 2.3: Talk
Thursday, September 11, 2025, 14:45–15:00, ZHG002
An infinite hierarchy of quantum-enhanced learning tasks — •Jan Nöller1, Viet Tran2, and Richard Kueng2 — 1Technische Universität Darmstadt — 2Johannes-Kepler-Universität Linz
Learning properties of quantum states from empirical data is arguably the most fundamental quantum learning challenge. Seminal work over the past years has shown that the sample complexity associated with such tasks strongly depends on the underlying measurement primitive. As an example, determining all Pauli-observables on an n-qubit becomes sample-efficient if we allow entangling measurements on pairs of state copies, where an exponential number of samples is required if only single-copy measurements are performed. Similar separations also apply to purity testing. However, so far it has been unclear whether such exponential separation results also hold for 3 or more state copies: are there learning tasks that must be exponentially hard for (k -1)-copy measurements, but become very efficient if we allow k-copy measurements? Here, we answer this question affirmatively for every k that is a prime number. The underlying learning challenges arise from carefully extending n-qubit Pauli tomography to Weyl-Heisenberg tomography on n qudits. Up to our knowledge, our findings describe the first infinite family of rigorous separation results for multi-copy state learning.
Keywords: Learning; Tomography; Complexity; Qudits