Continuous-variable ramp quantum secret sharing with Gaussian states and operations. (12th November 2019)

• Record Type: Journal Article
• Authors: Habibidavijani, Masoud; Sanders, Barry C
• Is Part Of: New journal of physics. Volume 21:Number 11(2019:Nov.)
• Publication Date: 2019-11-12
• Subjects: quantum secret sharing -- continuous-variable quantum information -- security of secret sharing protocols; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/ab4d9c
• Languages: English
• ISSNs: 1367-2630

Abstract

Abstract: We aim to quantify and mitigate quantum-information leakage in continuous-variable quantum secret sharing (CV QSS). Here we introduce a technique for certifying CV ramp quantum secret-sharing (RQSS) 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 CV QSS 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 CR quantum mutual information to obtain quantum mutual information in terms of squeezing. Our quantum mutual information result quantifies the leakage of the RQSS schemes.