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IMPERIAL COLLEGE PRESS eBooks

Quantum State Sharing with Continuous Variables

Tomáš Tyc, Barry C. Sanders, Thomas Symul, Warwick P. Bowen, Andrew M. Lance, Ping Koy Lam

Published Feb 1, 2007• 2 citations
Publisher
DOI
10.1142/9781860948169_0015

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Practical continuous-variable quantum secret sharing using plug-and-play dual-phase modulation

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Continuous-variable quantum secret sharing (CVQSS) allows a legitimate user, i.e., the dealer, to share a string of secret keys with multiple distant users. These users cannot individually recover the dealer's secret key unless they work cooperatively. Although the theoretical security proof of CVQSS has been well established, its practical security and implementation still face challenges. In this paper, we suggest a practical scheme for CVQSS using plug-and-play (P&P) configuration and dual-phase-modulated coherent state (DPMCS). The proposed scheme, called P&P DPM-based CVQSS, waives the necessity that each user has to prepare respective coherent states with their own lasers, thereby eliminating synchronous loopholes caused by different lasers and reducing the complexity of deployment of the user's stations. Moreover, the local oscillator (LO) can be generated locally by the dealer so that the whole CVQSS system could be naturally immune to all LO-aimed attacks. We derive the security bounds for P&P DPM-based CVQSS by properly making most of the existing security analysis techniques of continuous-variable quantum key distribution (CVQKD). In addition, an experimental concept of P&P DPM-based CVQSS is also presented, which can be deemed a guideline for future implementation.

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Continuous-Variable Ramp Quantum Secret Sharing with Gaussian States and Operations

Habibi Davijani, Masoud

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.

•Jan 1, 2019•11 citations

Quantum information with continuous variables

Nicolas J. Cerf

•Sep 12, 2006•4 citations
Continuous-variable quantum secret sharing (CVQSS) allows a legitimate user, i.e., the dealer, to share a string of secret keys with multiple distant users. These users cannot individually recover the dealer's secret key unless they work cooperatively. Although the theoretical security proof of CVQSS has been well established, its practical security and implementation still face challenges. In this paper, we suggest a practical scheme for CVQSS using plug-and-play (P&P) configuration and dual-phase-modulated coherent state (DPMCS). The proposed scheme, called P&P DPM-based CVQSS, waives the necessity that each user has to prepare respective coherent states with their own lasers, thereby eliminating synchronous loopholes caused by different lasers and reducing the complexity of deployment of the user's stations. Moreover, the local oscillator (LO) can be generated locally by the dealer so that the whole CVQSS system could be naturally immune to all LO-aimed attacks. We derive the security bounds for P&P DPM-based CVQSS by properly making most of the existing security analysis techniques of continuous-variable quantum key distribution (CVQKD). In addition, an experimental concept of P&P DPM-based CVQSS is also presented, which can be deemed a guideline for future implementation.
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.