New explicit constructions show exponential tightness of the product-versus-operator norm gap and noncommutative Bohnenblust-Hille constant, disprove the dimension-free quantum Fourier Entropy-Influence inequality, and prove the Aaronson-Ambainis bound for anti-commuting Pauli-string Hamiltonians.
Approximation algorithms for quantum many-body problems
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Tightness of and counterexamples to several quantum estimates
New explicit constructions show exponential tightness of the product-versus-operator norm gap and noncommutative Bohnenblust-Hille constant, disprove the dimension-free quantum Fourier Entropy-Influence inequality, and prove the Aaronson-Ambainis bound for anti-commuting Pauli-string Hamiltonians.