# A Class of PPT Entangled States Arbitrary Far From Separable States

## TL;DR

This paper constructs multipartite PPT entangled states that are arbitrarily far from separable states, showing that the trace distance can increase with local Hilbert space dimension without needing multiple copies.

## Contribution

It provides an explicit construction of multipartite PPT entangled states with large trace distance from separable states, advancing understanding of entanglement properties.

## Key findings

- Explicit multipartite PPT entangled states with large trace distance
- Distance from separable states increases with local Hilbert space dimension
- No need for multiple copies to achieve large trace distance

## Abstract

In this paper we show an explicit construction of multipartite class of entangled states with the PPT (Positive Partial Transposition) property in every cut. We investigate properties of this class of states focusing on the trace distance from the set of separable states. We provide an explicit sub-class of the multipartite entangled PPT states which are arbitrary far from the set of separable states. We argue, that in the multipartite case the mentioned distance increases with dimension of the local Hilbert space. In our construction is we do not have to use many copies of initial state living on the smaller space to boost the trace distance as in the previous attempts to this problem.