Noncommutative Bohnenblust--Hille Inequality for qudit systems

Previous noncommutative Bohnenblust--Hille (BH) inequalities addressed operator decompositions in the tensor-product space M₂(C)⊗ n; i.e., for systems of qubits {HCP22,VZ23}. Here we prove noncommutative BH inequalities for operators decomposed in tensor-product spaces of arbitrary local dimension, i.e., MK(C)⊗ n for any K≥2 or on systems of K-level qudits. We treat operator decompositions in both the Gell-Mann and Heisenberg--Weyl basis, reducing to the recently-proved commutative hypercube BH {DMP} and cyclic group BH {SVZ} inequalities respectively. As an application we discuss learning qudit quantum observables.