Estimating the Schmidt numbers of quantum states via symmetric measurements

TL;DR

This paper introduces a new criterion for estimating the Schmidt number of quantum states using symmetric measurements, which improves upon existing methods in quantifying entanglement.

Contribution

The authors develop a novel Schmidt number criterion based on the trace norm of the correlation matrix from symmetric measurements, enhancing entanglement quantification.

Findings

The new criterion outperforms existing methods in examples.

It provides a more effective way to estimate Schmidt numbers.

The approach is applicable to various quantum states.

Abstract

The Schmidt numbers quantify the entanglement degree of quantum states. Quantum states with high Schmidt numbers provide a larger advantage in various quantum information processing tasks compared to quantum states with low Schmidt numbers. We derive a Schmidt number criterion based on the trace norm of the correlation matrix obtained from symmetric measurements. We show that our result is more effective than and superior to existing Schmidt number criteria by detailed examples.