A note on Schmidt-number witnesses based on symmetric measurements

TL;DR

This paper introduces new Schmidt-number witnesses based on symmetric measurements, improving the detection of entanglement in high-dimensional quantum states and linking them with experimentally accessible tools like the Fedorov ratio.

Contribution

The authors derive a new class of k-positive linear maps for better Schmidt-number detection and demonstrate their effectiveness in high-dimensional quantum systems.

Findings

New Schmidt-number witnesses identify higher Schmidt numbers more effectively.

The Fedorov ratio can validate the new witnesses experimentally.

Enhanced detection of entanglement in complex quantum states.

Abstract

The Schmidt number is an important kind of characterization of quantum entanglement. Quantum states with higher Schmidt numbers demonstrate significant advantages in various quantum information processing tasks. By deriving a class of k-positive linear maps based on symmetric measurements, we present new Schmidt-number witnesses of class (k + 1). By detailed example, we show that our Schmidt number witnesses identify better the Schmidt number of quantum states in high-dimensional systems. Furthermore, we note that the Fedorov ratio, which coincides with the Schmidt number for pure Gaussian states and provides a close approximation in non-Gaussian cases such as spontaneous parametric down-conversion, serves as an experimentally accessible tool for validating the proposed (k +1)-class Schmidt-number witnesses.