Tight bounds and natural examples for quantum channel testing
Tight bounds and natural examples for quantum channel testing — original question and dated source context.
Problem statement
Distinguish an unknown maximally depolarizing -qubit channel from a fixed Haar-random unitary channel using adaptive prepare–apply–measure queries. Can the source’s lower bound be improved to a tight bound? Find other natural property-testing problems with interesting quantum advantages that do not rely on Haar-random unitaries or pseudorandom substitutes, for example low-depth circuits or local Hamiltonians.
Lean 4
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Progress & source assessment
Historical source dated 2024-10-27. Current resolution status has not been independently reassessed; bounds and claims in the source context refer to that date.
- [1]Chen, Cotler, Huang, Li and Tang, Some Open Problems in Quantum Learning, FOCS 2024 workshop, slide 9 link
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