Quantum advantage without entanglement (pp606-615)
         Dan Kenigsberg, Tal Mor, and Gil Ratsaby    
          doi: https://doi.org/10.26421/QIC6.7-4
Abstracts: We study the advantage of pure-state quantum computation without entanglement over classical computation. For the Deutsch-Jozsa algorithm we present the \emph{maximal} subproblem that can be solved without entanglement, and show that the algorithm still has an advantage over the classical ones. We further show that this subproblem is of greater significance, by proving that it contains all the Boolean functions whose quantum phase-oracle is non-entangling. For Simon's and Grover's algorithms we provide simple proofs that no non-trivial subproblems can be solved by these algorithms without entanglement.
Key words: quantum algorithms, entanglement, tensor product states, separability