The elusive source of quantum effectiveness

TL;DR

This paper investigates the roles of quantum correlations and state distinguishability in quantum information processing, highlighting their complex interplay especially in mixed states and various quantum algorithms.

Contribution

It provides a nuanced analysis of how quantum correlations and distinguishability contribute to quantum computational efficiency, especially in mixed states and cluster states.

Findings

Quantum correlations are essential for pure state manipulations.

Distinguishability plays a key role in mixed state quantum processing.

Entanglement's role in cluster states is counter-intuitive and complex.

Abstract

We discuss two qualities of quantum systems: various correlations existing between their subsystems and the distingushability of different quantum states. This is then applied to analysing quantum information processing. While quantum correlations, or entanglement, are clearly of paramount importance for efficient pure state manipulations, mixed states present a much richer arena and reveal a more subtle interplay between correlations and distinguishability. The current work explores a number of issues related with identifying the important ingredients needed for quantum information processing. We discuss the Deutsch-Jozsa algorithm, the Shor algorithm, the Grover algorithm and the power of a single qubit class of algorithms. One section is dedicated to cluster states where entanglement is crucial, but its precise role is highly counter-intuitive. Here we see that distinguishability becomes a more useful concept.