# Family of Bell inequalities violated by higher-dimensional bound entangled states

## TL;DR

This paper introduces a family of Bell inequalities that are violated by higher-dimensional bound entangled states, suggesting these inequalities can serve as dimension witnesses for such states.

## Contribution

The authors construct new Bell inequalities for higher-dimensional systems and propose their use as dimension witnesses for bound entangled states, supported by numerical evidence.

## Key findings

- Bell inequalities violated by bound entangled states for all d>2
- Numerical support for the dimension witness conjecture up to d=8
- Potential for these inequalities to identify the Hilbert space dimension of bound entangled states

## Abstract

We construct ($d\times d$)-dimensional bound entangled states, which violate, for any $d>2$, a bipartite Bell inequality introduced in this paper. We conjecture that the proposed class of Bell inequalities acts as a dimension witness for bound entangled states: For any $d>2$ there exists a Bell inequality from this class that can be violated with bound entangled states only if their Hilbert space dimension is at least $d\times d$. Numerics supports this conjecture up to $d=8$.