The GHZ state in secret sharing and entanglement simulation

TL;DR

This paper explores properties of the GHZ state, introduces an efficient quantum secret sharing protocol using classical channels, and analyzes the communication complexity for simulating GHZ states classically.

Contribution

It presents a novel quantum secret sharing scheme requiring only classical channels and establishes lower bounds on classical simulation of GHZ states.

Findings

Quantum secret sharing with classical channels is more efficient than teleportation.

Classical simulation of n-party GHZ states requires at least n log n - 2n bits.

A simplified problem related to GHZ simulation may lead to a no-go theorem.

Abstract

In this note, we study some properties of the GHZ state. First, we present a quantum secret sharing scheme in which the participants require only classical channels in order to reconstruct the secret; our protocol is significantly more efficient than the trivial usage of teleportation. Second, we show that the classical simulation of an n-party GHZ state requires at least n log n - 2n bits of communication. Finally, we present a problem simpler than the complete simulation of the multi-party GHZ state, that could lead to a no-go theorem for GHZ state simulation.