Quantum Advantage without Entanglement

We study the advantage of pure-state quantum computation without entanglement over classical computation. For the Deutsch-Jozsa algorithm we present the 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.Comment: 10 page

Classicality and Quantumness in Quantum Information Processing

The research thesis was done under the supervision of Dr. Tal Mor in the Computer Science Department. I thank Tal Mor for his guidance throughout the course of this research. Michel Boyer and Berry Groisman deserve special thanks; without their tremendous support, this work would not have been concluded, and obviously to my wife Karmit. I would also like to thank Gilad Ben-Avi, Eli Biham, Gili Bisker, Gille