Quantum secret sharing with continuous-variable cluster states

TL;DR

This paper extends cluster state quantum secret sharing to continuous variables, analyzing security and performance with finitely squeezed states and proposing benchmarks for practical implementation.

Contribution

It introduces a continuous-variable framework for quantum secret sharing, including security analysis and performance metrics for realistic, finitely squeezed states.

Findings

Infinite squeezing ensures perfect security against adversaries.

Finitely squeezed states leak some secret information, affecting security.

Benchmarks are proposed to evaluate security in practical scenarios.

Abstract

We extend the formalism of cluster state quantum secret sharing, as presented in Markham and Sanders [Phys. Rev. A 78, 042309 (2008)] and Keet et al. [Phy. Rev. A 82, 062315 (2010)], to the continuous-variable regime. We show that both classical and quantum information can be shared by distributing continuous-variable cluster states through either public or private channels. We find that the adversary structure is completely denied from the secret if the cluster state is infinitely squeezed, but some secret information would be leaked if a realistic finitely squeezed state is employed. We suggest benchmarks to evaluate the security in the finitely squeezed cases. For the sharing of classical secrets, we borrow techniques from the continuous-variable quantum key distribution to compute the secret sharing rate. For the sharing of quantum states, we estimate the amount of entanglement distilled for teleportation from each cluster state.