# Device Independent Quantum Secret Sharing in Arbitrary Even Dimension

## TL;DR

This paper introduces a device independent quantum secret sharing scheme for arbitrary even dimensions, leveraging multipartite Bell inequalities and entanglement properties to ensure security and correctness.

## Contribution

It generalizes quantum secret sharing to higher even dimensions using a novel multipartite Bell inequality and provides security proofs based on entanglement polygamy.

## Key findings

- Scheme is $psilon_{cor}$-correct and $psilon^c$-complete.
- Security relies on causal independence and entanglement properties.
- Probability of winning the linear game tests device independence.

## Abstract

We present a device independent quantum secret sharing scheme in arbitrary even dimension. We propose a $d$-dimensional $N$-partite linear game, utilizing a generic multipartite higher dimensional Bell inequality, a generalization of Mermin's inequality in the higher dimension. Probability to win this linear game defines the device independence test of the proposed scheme. The security is proved under causal independence of measurement devices and it is based on the polygamy property of entanglement. By defining $\epsilon_{cor}$-correctness and $\epsilon^c$-completeness for a quantum secret sharing scheme, we have also shown that the proposed scheme is $\epsilon_{cor}$-correct and $\epsilon^c$-complete.