On the Necessity of Entanglement for the Explanation of Quantum Speedup

TL;DR

This paper argues that entanglement is essential for explaining quantum speedup, countering claims that certain models can achieve speedup without entanglement by analyzing specific examples.

Contribution

It clarifies the role of entanglement in quantum speedup and refutes claims that some quantum models operate without it.

Findings

Entanglement is necessary for quantum speedup.

Counter-examples do not prove entanglement is unnecessary.

Examples clarify the role of entanglement in quantum computation.

Abstract

In this paper I argue that entanglement is a necessary component for any explanation of quantum speedup and I address some purported counter-examples that some claim show that the contrary is true. In particular, I address Biham et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill & Laflamme's deterministic quantum computation with one qubit (DQC1) model of quantum computation. I argue that these examples do not demonstrate that entanglement is unnecessary for the explanation of quantum speedup, but that they rather illuminate and clarify the role that entanglement does play.