Optimal approximate transpose map via quantum designs and its applications to entanglement detection

TL;DR

This paper demonstrates that quantum designs can optimally approximate the transpose map, enabling practical applications in entanglement detection through measurement-and-preparation schemes.

Contribution

It introduces a quantum design-based method for optimal approximate transpose maps and applies it to multipartite entanglement detection.

Findings

Quantum designs characterize optimal transpose approximations.

Measurement-and-preparation schemes implement the approximate transpose.

Applications include detecting multipartite entangled states.

Abstract

We show that quantum designs characterize the general structure of the optimal approximation of the transpose map on quantum states. Based on this characterization, we propose an implementation of the approximate transpose map by a measurement-and-preparation scheme. The results show that state-manipulation in quantum two-designs suffices for transpose-based quantu3 information applications. In particular, we present how these results can be applied to the framework of detecting multipartite entangled states, for instance, when local measurements or interferometry-based experimental approaches are applied.