The controlled SWAP test for determining quantum entanglement

TL;DR

This paper introduces a controlled SWAP test adapted for efficiently detecting and classifying quantum entanglement in pure states, with fewer copies needed for larger systems and robustness to small errors.

Contribution

It develops a novel entanglement detection method based on the controlled SWAP test, capable of identifying entanglement classes and relating to concurrence, with improved efficiency for large systems.

Findings

Detects entanglement and genuine n-qubit entanglement

Number of copies needed decreases with system size for maximally entangled states

Method is robust to small state preparation errors

Abstract

Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a pure state. Here we show that the test can evidence the presence of entanglement (and further, genuine n-qubit entanglement), can distinguish entanglement classes, and that the concurrence of a two-qubit state is related to the test's output probabilities. We also propose a multipartite measure of entanglement that acts similarly for n-qubit states. The number of copies required to detect entanglement decreases for larger systems, to four on average for many (n>8) qubits for maximally entangled states. For non-maximally entangled states, the average number of copies of the test state required to detect entanglement increases with decreasing entanglement. Furthermore, the results are robust to second order when typical small errors are introduced to the state under investigation.