Quantum states for perfectly secure secret sharing

TL;DR

This paper characterizes the quantum states suitable for perfectly secure secret sharing, establishing conditions, and demonstrating their distillability properties, including the ability to produce GHZ states and states with minimal bipartite entanglement.

Contribution

It provides necessary and sufficient conditions for quantum states to enable perfect secret sharing and analyzes their distillability features, including a novel class with minimal bipartite entanglement.

Findings

States are bipartite distillable for all splits.

States can be distilled into GHZ states.

Existence of secret-sharing states with arbitrarily small bipartite entanglement.

Abstract

In this work, we investigate what kinds of quantum states are feasible to perform perfectly secure secret sharing, and present its necessary and sufficient conditions. We also show that the states are bipartite distillable for all bipartite splits, and hence the states could be distillable into the Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing states, which have an arbitrarily small amount of bipartite distillable entanglement for a certain split.