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arXiv:quant-ph/0210188 · New Journal of Physics

Continuous variable (2, 3) threshold quantum secret sharing schemes

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

Published Jan 17, 2003• 58 citations
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Abstract

We present two schemes to perform continuous variable (2, 3) threshold quantum secret sharing (QSS) on the quadrature amplitudes of bright light beams. Both schemes require a pair of entangled light beams. The first scheme utilizes two phase sensitive optical amplifiers, whilst the second uses an electro-optic feedforward loop for the reconstruction of the secret. We examine the efficacy of QSS in terms of fidelity, as well as the signal transfer coefficients and the conditional variances of the reconstructed output state. We show that both schemes in the ideal case yield perfect secret reconstruction.

DOI
10.1088/1367-2630/5/1/304

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We present two schemes to perform continuous variable (2, 3) threshold quantum secret sharing (QSS) on the quadrature amplitudes of bright light beams. Both schemes require a pair of entangled light beams. The first scheme utilizes two phase sensitive optical amplifiers, whilst the second uses an electro-optic feedforward loop for the reconstruction of the secret. We examine the efficacy of QSS in terms of fidelity, as well as the signal transfer coefficients and the conditional variances of the reconstructed output state. We show that both schemes in the ideal case yield perfect secret reconstruction.
We present an experimental scheme to perform continuous variable (2,3) threshold quantum secret sharing on the quadratures amplitudes of bright light beams. It requires a pair of entangled light beams and an electro-optic feedforward loop for the reconstruction of the secret. We examine the efficacy of quantum secret sharing in terms of fidelity, as well as the signal transfer coefficients and the conditional variances of the reconstructed output state. We show that, in the ideal limit, perfect secret reconstruction is possible. We discuss two different definitions of quantum secret sharing: the sharing of a quantum secret and the sharing of a classical secret with quantum resources.
Quantum state sharing, an important protocol in quantum information, can enable secure state distribution and reconstruction when part of the information is lost. In (k, n) threshold quantum state sharing, the secret state is encoded into n shares and then distributed to n players. The secret state can be reconstructed by any k players (k > n / 2), while the rest of the players get nothing. In the continuous variable regime, the implementation of quantum state sharing needs the feedforward technique, which involves optic-electro and electro-optic conversions. These conversions limit the bandwidth of the quantum state sharing. Here, to avoid the optic-electro and electro-optic conversions, we experimentally demonstrate (2, 3) threshold deterministic all-optical quantum state sharing. A low-noise phase-insensitive amplifier based on the four-wave mixing process is utilized to replace the feedforward technique. We experimentally demonstrate that any two of three players can cooperate to implement the reconstruction of the secret state, while the rest of the players cannot get any information. Our results provide an all-optical platform to implement arbitrary (k, n) threshold deterministic all-optical quantum state sharing and pave the way to construct the all-optical broadband quantum network.
We develop the theory of continuous-variable quantum secret sharing and propose its interferometric realization using passive and active optical elements. In the ideal case of infinite squeezing, a fidelity F\mathcal{F}F of unity can be achieved with respect to reconstructing the quantum secret. We quantify the reduction in fidelity for the (2,3) threshold scheme due to finite squeezing and establish the condition for verifying that genuine quantum secret sharing has occurred.
Quantum secret sharing (QSS) can usually realize unconditional security with entanglement of quantum systems. While the usual security proof has been established in theoretics, how to defend against the tolerable channel loss in practices is still a challenge. The traditional ( t , n ) threshold schemes are equipped in situation where all participants have equal ability to handle the secret. Here we propose an improved ( t , n ) threshold continuous variable (CV) QSS scheme using weak coherent states transmitting in a chaining channel. In this scheme, one participant prepares for a Gaussian-modulated coherent state (GMCS) transmitted to other participants subsequently. The remaining participants insert independent GMCS prepared locally into the circulating optical modes. The dealer measures the phase and the amplitude quadratures by using double homodyne detectors, and distributes the secret to all participants respectively. Special t out of n participants could recover the original secret using the Lagrange interpolation and their encoded random numbers. Security analysis shows that it could satisfy the secret sharing constraint which requires the legal participants to recover message in a large group. This scheme is more robust against background noise due to the employment of double homodyne detection, which relies on standard apparatuses, such as amplitude and phase modulators, in favor of its potential practical implementations.
Quantum secret sharing (QSS) allows multiple players to achieve unconditional secure communication through an unsecure quantum channel; however, the actual implementation requires a modulator with a high extinction ratio, which means high system expense and miniaturization and commercialization difficulties. In this paper, we propose a continuous variable QSS scheme that can replace the traditional lasers and modulators with directly modulated lasers (DML). Each player prepares quantum states through a DML and sends the signal light to the dealer through a beam splitter into a quantum channel. The method provides a new way for realizing secret key sharing. Moreover, we introduce the chirp estimation algorithm to realize the phase modulation, which can achieve a two-dimensional modulation scheme under a single laser.
Abstract Quantum secret sharing (QSS), as a fundamental cryptographic protocol for future quantum networks, continues to face significant challenges, particularly in the generation of multipartite entanglement and the degradation of entanglement fidelity during distribution, both of which severely limit its scalability. These persistent constraints motivate an alternative approach based on continuous-variable (CV) systems. We propose a CVQSS scheme based on an electro-optically modulated optical frequency comb. The scheme employs a single laser to generate multi-wavelength coherent states, enabling the efficient and flexible construction of secret sharing subnetworks. By incorporating a broadcast-based distribution mechanism, the architecture is scalable to 128 players. Experimental verification with 24 players over a 10 km fiber link demonstrates a secret sharing rate of 6.24 per player under asymptotic conditions and 1.27 Mbps per player under finite-size effects, and a 1.05MB image is secretly shared to six players. This work achieves information-theoretically secure QSS both within and across subnetworks, providing a solid technical foundation for the development of scalable and multifunctional quantum networks.