# A class of genuinely high-dimensionally entangled states with a positive partial transpose

## TL;DR

This paper investigates high-dimensional PPT entangled states, demonstrating that their Schmidt number can scale linearly with the local dimension, revealing stronger entanglement properties than previously thought.

## Contribution

It generalizes methods to calculate Schmidt numbers of PPT states, showing linear scaling with local dimension in high-dimensional systems.

## Key findings

- Schmidt number scales linearly with dimension d
- High-dimensional PPT states can exhibit strong entanglement
- Generalized methods for Schmidt number calculation

## Abstract

Entangled states with a positive partial transpose (so-called PPT states) are central to many interesting problems in quantum theory. On one hand, they are considered to be weakly entangled, since no pure state entanglement can be distilled from them. On the other hand, it has been shown recently that some of these PPT states exhibit genuinely high-dimensional entanglement, i.e. they have a high Schmidt number. Here we investigate $d\times d$ dimensional PPT states for $d\ge 4$ discussed recently by Sindici and Piani, and by generalizing their methods to the calculation of Schmidt numbers we show that a linear $d/2$ scaling of its Schmidt number in the local dimension $d$ can be attained.