A new construction of flat degree-d Hamiltonians with exp(Theta(d^2)) nonzero Pauli terms makes the noncommutative Bohnenblust-Hille constant exponential and refutes the quantum Fourier Entropy-Influence conjecture.
Noncommutative Bohnenblust–Hille inequalities , volume =
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Dense Hamiltonians at the Parseval Limit: The Noncommutative BH Constant is Exponential and the Quantum FEI Conjecture is False
A new construction of flat degree-d Hamiltonians with exp(Theta(d^2)) nonzero Pauli terms makes the noncommutative Bohnenblust-Hille constant exponential and refutes the quantum Fourier Entropy-Influence conjecture.