We propose a continuous-variable quantum secret sharing scheme based on multi-ring discrete modulation, which we called MR-CVQSS. In this scheme, phase shift keying (PSK)-modulated coherent states are allowed to be further discretely modulated with different amplitudes, so that these modulated coherent states can be scattered on different amplitude rings in phase space. The advantage for this multi-ring structure is that the error probability of quantum detector for discriminating discretely-modulated coherent states (DMCSs) is more lower than that of original single-ring discretely modulated CVQSS, which is beneficial for improving the performance of whole CVQSS system. We derive the security bound for MR-CVQSS against both eavesdroppers and dishonest users, and the numerical simulation shows that the performance of MR-CVQSS in terms of both maximal transmission distance and maximal available number of users can be largely improved. Moreover, security analysis shows that the modulation variance of MR-CVQSS does not need to be very small, thereby improving the signal-to-noise ratio (SNR) of whole CVQSS system.
We propose a continuous-variable quantum secret sharing scheme based on multi-ring discrete modulation, which we called MR-CVQSS. In this scheme, phase shift keying (PSK)-modulated coherent states are allowed to be further discretely modulated with different amplitudes, so that these modulated coherent states can be scattered on different amplitude rings in phase space. The advantage for this multi-ring structure is that the error probability of quantum detector for discriminating discretely-modulated coherent states (DMCSs) is more lower than that of original single-ring discretely modulated CVQSS, which is beneficial for improving the performance of whole CVQSS system. We derive the security bound for MR-CVQSS against both eavesdroppers and dishonest users, and the numerical simulation shows that the performance of MR-CVQSS in terms of both maximal transmission distance and maximal available number of users can be largely improved. Moreover, security analysis shows that the modulation variance of MR-CVQSS does not need to be very small, thereby improving the signal-to-noise ratio (SNR) of whole CVQSS system.
Abstract In order to avoid the complexity of Gaussian modulation and the problem that the traditional point-to-point communication DM-CVQKD protocol cannot meet the demand for multi-user key sharing at the same time, we propose a multi-ring discrete modulation continuous variable quantum key sharing scheme (MR-DM-CVQSS). In this paper, we primarily compare single-ring and multi-ring M-symbol amplitude and phase-shift keying modulations. We analyze their asymptotic key rates against collective attacks and consider the security key rates under finite-size effects. Leveraging the characteristics of discrete modulation, we improve the quantum secret sharing scheme. Non-dealer participants only require simple phase shifters to complete quantum secret sharing. We also provide the general design of the MR-DM-CVQSS protocol. We conduct a comprehensive analysis of the improved protocol’s performance, confirming that the enhancement through multi-ring M-PSK allows for longer-distance quantum key distribution. Additionally, it reduces the deployment complexity of the system, thereby increasing the practical value.
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.
We propose a continuous-variable measurement-device-independent quantum key distribution with multi-ring discrete modulation (MR-CV-MDI-QKD) protocol. In our scheme, coherent states are allocated across distinct rings (amplitudes) in the phase space, and each ring is subjected to traditional M-symbol phase shift keying (MPSK) modulation. The analysis and simulation are given to demonstrate the security of our scheme under collective attacks. The results show that, compared with the traditional discrete modulated (DM)-CV-MDI-QKD where only the MPSK is used for modulation with a fixed amplitude, MR-CV-MDI-QKD can decrease the upper bound of the information accessible to an eavesdropper, thereby facilitating an extended transmission distance and increasing the secret key rate, furthermore, it exhibits a higher tolerance to diminished reverse reconciliation efficiency. This work provides an effective way for the practical implementation of the CV-MDI-QKD protocol.
Abstract Continuous-variable quantum secret sharing (CVQSS) is a promising approach to ensuring multi-party information security. While CVQSS offers practical ease of implementation, its present performance remains limited. In this paper, we propose a novel CVQSS protocol integrated with a state-discrimination detector (SDD), dubbed SDD-CVQSS. In particular, we first develop the detailed procedure of SDD-CVQSS, which replaces the traditional coherent detector with an SDD and eliminates the long-standing necessary step of establishing multiple point-to-point quantum key distribution links between all users and the dealer. We then elaborate on the principle of the specifically designed SDD, which can efficiently discriminate interfered states with a much lower error probability. Finally, we construct a security model for SDD-CVQSS and derive its security bound against both eavesdroppers and dishonest users. Numerical simulations show that SDD-CVQSS outperforms conventional CVQSS in terms of both maximum transmission distance and secret key rate, and its performance is even superior to the PLOB bound. Additionally, we find that the performance degradation of SDD-CVQSS in long-distance transmission scenarios can be effectively compensated for using a post-selection scheme, providing a feasible way to achieve high-performance CVQSS.
Point-to-point quantum privacy communication over a standard telecommunication fiber link can be implemented by continuous-variable quantum key distribution (CV QKD). However, as communication networks develop, the two-party CV QKD system may hardly meet the requirements of secret key sharing of multiple users (at least three users). In this paper, we consider a protocol called quantum secret sharing (QSS) which allows a legitimate user, a so-called dealer, to share a secret key with multiple remote users through an insecure quantum channel. These users can correctly recover the dealer's secret key only when they work cooperatively. We carry out QSS with discretely modulated coherent states (DMCSs) because they are easy to prepare and resilient to losses. An asymptotic security proof for the proposed DMCS-based QSS protocol against both eavesdroppers and dishonest users is presented. Numerical simulation based on a linear bosonic channel shows that the maximal transmission distance of the DMCS-based QSS protocol reaches more than 100 km, and it can be further lengthened by exploiting a higher-dimensional discrete modulation strategy. Moreover, the composable security of the DMCS-based QSS protocol is also presented.
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.