Entanglement and deterministic quantum computing with one qubit

TL;DR

This paper introduces new tools to analyze entanglement in complex quantum systems, demonstrating that certain quantum algorithms can outperform classical ones without generating entanglement.

Contribution

It provides novel methods for studying entanglement in mixed, degenerate states and applies them to DQC1, showing these states can be computationally powerful despite limited entanglement.

Findings

DQC1 states have eigenvalue structures that hinder entanglement.

Quantum advantage may exist without entanglement generation.

New tools improve understanding of quantum correlations in mixed states.

Abstract

The role of entanglement and quantum correlations in complex physical systems and quantum information processing devices has become a topic of intense study in the past two decades. In this work we present new tools for learning about entanglement and quantum correlations in dynamical systems where the quantum states are mixed and the eigenvalue spectrum is highly degenerate. We apply these results to the Deterministic quantum computing with one qubit (DQC1) computation model and show that the states generated in a DQC1 circuit have an eigenvalue structure that makes them difficult to entangle, even when they are relatively far from the completely mixed state. Our results strengthen the conjecture that it may be possible to find quantum algorithms that do not generate entanglement and yet still have an exponential advantage over their classical counterparts.