# Continuous-variable ramp quantum secret sharing with Gaussian states and operations

## TL;DR

This paper develops a framework for continuous-variable ramp quantum secret sharing using Gaussian states, introduces a certification procedure via quantum interactive proofs, and quantifies information leakage through quantum mutual information.

## Contribution

It formulates a new continuous-variable ramp quantum secret sharing protocol with a certification method and derives a formula for quantum mutual information to assess security.

## Key findings

- Certification procedure for ramp quantum secret sharing schemes
- Expression for quantum mutual information in terms of squeezing
- Quantification of information leakage in the scheme

## Abstract

Our aim is to formulate continuous-variable quantum secret sharing as a continuous-variable ramp quantum secret sharing protocol, provide a certification procedure for it and explain the criteria for the certification. Here we introduce a technique for certifying continuous-variable ramp quantum secret-sharing schemes in the framework of quantum interactive-proof systems. We devise pseudocodes in order to represent the sequence of steps taken to solve the certification problem. Furthermore, we derive the expression for quantum mutual information between the quantum secret extracted by any multi-player structure and the share held by the referee corresponding to the Tyc-Rowe-Sanders continuous-variable quantum secret-sharing scheme. We solve by converting the Tyc-Rowe-Sanders position representation for the state into a Wigner function from which the covariance matrix can be found, then insert the covariance matrix into the standard formula for continuous-variable quantum mutual information to obtain quantum mutual information in terms of squeezing. Our quantum mutual information result quantifies the leakage of the ramp quantum secret-sharing schemes.