Schmidt number criterion via general symmetric informationally complete measurements

TL;DR

This paper introduces a new Schmidt number criterion based on symmetric informationally complete measurements, providing a more effective way to quantify entanglement in bipartite quantum states across various dimensions.

Contribution

The authors develop a novel Schmidt number criterion using the trace norm of the correlation matrix from SIC measurements, outperforming existing criteria in certifying entanglement.

Findings

The criterion effectively quantifies entanglement dimension.

It outperforms fidelity, CCNR, MUB, and EAM criteria.

Demonstrated superiority through detailed examples.

Abstract

The Schmidt number characterizes the quantum entanglement of a bipartite mixed state and plays a significant role in certifying entanglement of quantum states. We derive a Schmidt number criterion based on the trace norm of the correlation matrix obtained from the general symmetric informationally complete measurements. The criterion gives an effective way to quantify the entanglement dimension of a bipartite state with arbitrary local dimensions. We show that this Schmidt number criterion is more effective and superior than other criteria such as fidelity, CCNR (computable cross-norm or realignment), MUB (mutually unbiased bases) and EAM (equiangular measurements) criteria in certifying the Schmidt numbers by detailed examples.