Quantum Secret Sharing with Continuous Variable Graph State

TL;DR

This paper analyzes practical quantum secret sharing protocols using continuous variable graph states, focusing on implementation, error estimation, and conditions for perfect secret reconstruction and security.

Contribution

It introduces implementation protocols for various QSS schemes with CVGS, derives explicit error estimates, and establishes conditions for perfect reconstruction and security thresholds.

Findings

Perfect reconstruction requires infinite squeezing.

Conditions for threshold protocols on weighted CVGS are derived.

Exclusive perfect reconstruction for non-cooperative groups is demonstrated.

Abstract

In this paper we study the protocol implementation and property analysis for several practical quantum secret sharing (QSS) schemes with continuous variable graph state (CVGS). For each QSS scheme, an implementation protocol is designed according to its secret and communication channel types. The estimation error is derived explicitly, which facilitates the unbiased estimation and error variance minimization. It turns out that only under infinite squeezing can the secret be perfectly reconstructed. Furthermore, we derive the condition for QSS threshold protocol on a weighted CVGS. Under certain conditions, the perfect reconstruction of the secret for two non-cooperative groups is exclusive, i.e. if one group gets the secret perfectly, the other group cannot get any information about the secret.