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.
Highlights
IntroductionWe provide the required context to tackle the problem that is solved in this thesis
1.1 BackgroundThis section provides the required context to tackle the problem that is solved in this thesis
We develop the quantum mutual information for the CV ramp quantum secret-sharing (CV RQSS) quantum access structures and employ it to quantify quantum-information leakage for Gaussian states and operations
Summary
We provide the required context to tackle the problem that is solved in this thesis. 1.1.1 is to present the key notions of quantum mutual information, which is the method for quantifying information security and defining quantum secret sharing, and plays a starring role in this thesis. I begin by presenting salient facts about Shannon and von Neumann entropies, which are the cornerstone of classical and quantum information theories, respectively. I present requisite knowledge concerning classical and quantum mutual information. 1.1.2, I review the main results on the theory of classical secret sharing. 1.1.2.2, I discuss the theory of discrete and continuous-variable quantum secret sharing. 1.2 I explain the aim, claim, novelty and importance of the problem, that has been solved in this thesis.
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