Continuous variable quantum secret sharing (CV-QSS) technologies are described that use laser sources and homodyne detectors. Here, a Gaussian-modulated coherent state (GMCS) prepared by one device passes through secure stations of other devices sequentially on its way to a trusted device, and each of the other devices coherently adds a locally prepared, independent GMCS to the group of propagating GMCSs. Finally, the trusted device measures both the amplitude and the phase quadratures of the received group of coherent GMCSs using double homodyne detectors. The trusted device suitably uses the measurement results to establish a secure key for encoding secret messages to be broadcast to the other devices. The devices cooperatively estimate, based on signals corresponding to their respective Gaussian modulations, the trusted device's secure key, so that the cooperative devices can decode the broadcast secret messages with the secure key.
Continuous variable quantum secret sharing (CV-QSS) technologies are described that use laser sources and homodyne detectors. Here, a Gaussian-modulated coherent state (GMCS) prepared by one device passes through secure stations of other devices sequentially on its way to a trusted device, and each of the other devices coherently adds a locally prepared, independent GMCS to the group of propagating GMCSs. Finally, the trusted device measures both the amplitude and the phase quadratures of the received group of coherent GMCSs using double homodyne detectors. The trusted device suitably uses the measurement results to establish a secure key for encoding secret messages to be broadcast to the other devices. The devices cooperatively estimate, based on signals corresponding to their respective Gaussian modulations, the trusted device's secure key, so that the cooperative devices can decode the broadcast secret messages with the secure key.
Secret sharing allows a trusted party (the dealer) to distribute a secret to a group of players, who can only access the secret cooperatively. Quantum secret sharing (QSS) protocols could provide unconditional security based on fundamental laws in physics. While the general security proof has been established recently in an entanglement-based QSS protocol, the tolerable channel loss is unfortunately rather small. Here we propose a continuous variable QSS protocol using conventional laser sources and homodyne detectors. In this protocol, a Gaussian-modulated coherent state (GMCS) prepared by one player passes through the secure stations of the other players sequentially, and each of the other players injects a locally prepared, independent GMCS into the circulating optical mode. Finally, the dealer measures both the amplitude and the phase quadratures of the receiving optical mode using double homodyne detectors. Collectively, the players can use their encoded random numbers to estimate the measurement results of the dealer and further generate a shared key. We prove the unconditional security of the proposed protocol against both eavesdroppers and dishonest players in the presence of high channel loss, and discuss various practical issues.
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.
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.
Although quantum key distribution (QKD) enables information-theoretically secure key distribution, it is mainly designed for point-to-point communication and cannot directly support multi-user collaborative scenarios. To address this limitation, quantum secret sharing (QSS) has been proposed to enable secure multiparty key sharing. However, most existing QSS protocols rely on a single-input single-output (SISO) channel, which limits the achievable secret key rate (SKR) and transmission distance. This paper proposes a continuous-variable (CV) QSS protocol based on a multiple-input multiple-output (MIMO) architecture operating in the terahertz (THz) band. In the proposed scheme, transmit-receive beamforming decomposes the MIMO channel into multiple parallel SISO subchannels, thereby improving both the SKR and transmission distance. We describe the QSS transmission procedure and derive the SKR expressions for eight protocol variants under Gaussian collective attacks. Specifically, Gaussian modulation and passive modulation are considered at the transmitter, while homodyne and heterodyne detection are considered at the receiver. Both asymptotic and composable finite-size SKR formulas are derived to characterize the ideal upper-bound performance and the achievable performance under finite resources, respectively. Simulation results show that, under ideal assumptions including perfect channel state information, perfect phase synchronization, and ideal beamforming, the Gaussian-modulation protocol with a 32 x 32 antenna configuration and the passive-modulation protocol with a 1024 x 1024 antenna configuration achieve transmission distances of 14.99 m and 160 m in the atmospheric channel, respectively. These results provide an idealized theoretical benchmark for evaluating the potential performance gains of MIMO-assisted THz CV-QSS in indoor and short-range outdoor wireless networks.
Continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) allows remote parties to share information-theoretical secure keys while defending all the side-channel attacks on measurement devices. However, the secure transmission distance and the secret key rate are quite limited due to the high untrusted equivalent excess noise in the Gaussian modulation. More particularly, extremely high-efficiency homodyne detections are required for even non-zero secure transmission distances, which directly restrict its practical realization. Here, we propose a CV-MDI-QKD protocol by encoding the key information into matched discrete phases of two groups of coherent states, which decreases the required detection efficiency for ideally asymmetric cases, and makes it possible to practically achieve secure key distribution with current low-efficiency homodyne detections. Besides, a proof-of-principle experiment with a locally generated oscillator is implemented, which, for the first time, demonstrates the realizability of CV-MDI-QKD using all fiber-based devices. The discrete-modulated phase-matching method provides an alternative direction of an applicable quantum key distribution with practical security.
Continuous-variable quantum secret sharing (CVQSS) based on discrete modulation is a viable alternative to Gaussian-modulated CVQSS due to its implementation simplicity. However, its theoretical performance remains far below the Gaussian-modulated counterparts. In this work we propose a CVQSS scheme based on constellation shaping, which enables near-Gaussian modulation effects by combining probabilistic and geometric constellation shaping with quadrature amplitude modulation (QAM). For the probabilistic shaping, binomial distribution and Boltzmann-Maxwell (BM) distribution are selected to adjust the occurrence probabilities of quantum states, and for the geometric shaping, triangular quadrature amplitude modulation (TQAM) is employed to optimize the geometric positions of the constellation points. Numerical simulations indicate that compared with other discrete-modulated CVQSS schemes, the proposed BM-distributed 16-TQAM scheme achieves the highest asymptotic secret key rate and the lowest detection error probability. Moreover, the optimal modulation variance of this scheme is higher than that of other schemes, demonstrating that the players can employ a larger modulation variance when preparing coherent states, thereby enhancing the signal-to-noise ratio of the whole system and providing a potential advantage in long-distance transmission.