Entanglement Sharing Protocol via Quantum Error Correcting Codes

TL;DR

This paper introduces entanglement sharing schemes using quantum error correcting codes, enabling controlled distribution of entanglement among multiple parties, with applications in quantum secret sharing and information leakage characterization.

Contribution

It proposes a new cryptographic protocol based on quantum error correcting codes, providing bounds, explicit examples, and applications in quantum secret sharing.

Findings

Lower bound on share size established

Constructed examples using Shor's code and stabilizer codes

Application to characterize leaked information in quantum ramp secret sharing

Abstract

We introduce a new multiparty cryptographic protocol, which we call `entanglement sharing schemes', wherein a dealer retains half of a maximally-entangled bipartite state and encodes the other half into a multipartite state that is distributed among multiple players. In a close analogue to quantum secret sharing, some subsets of players can recover maximal entanglement with the dealer whereas other subsets can recover no entanglement (though they may retain classical correlations with the dealer). We find a lower bound on the share size for such schemes and construct two non-trivial examples based on Shor's $[[9,1,3]]$ and the $[[4,2,2]]$ stabilizer code; we further demonstrate how other examples may be obtained from quantum error correcting codes through classical encryption. Finally, we demonstrate that entanglement sharing schemes can be applied to characterize leaked information in quantum ramp secret sharing.