Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2607.08158

Continuous-Variable MIMO THz Quantum Secret Sharing: Gaussian-modulation and Passive-modulation

Leixin Wu, Jiayu Pan, Fangzhe Chen, Lingtao Zhang, Bowen Zheng, Tie Qiu

quant-phSubmitted Jul 9, 2026• Announced Jul 10, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

Related papers

Continuous-variable Measurement Device Independent MIMO Quantum Key Distribution for THz Communications

Leixin Wu, Congtian Deng, Jiayu Pan +6 more

Although multiple-input multiple-output (MIMO) terahertz (THz) continuous-variable quantum key distribution (CVQKD) is theoretically secure, practical vulnerabilities may arise due to detector imperfections. This paper explores a CV measurement-device-independent (MDI) QKD system operating at THz frequencies within a MIMO framework. In this system, measurement is delegated to an untrusted third party, Charlie, rather than the receiver, eliminating all detector attacks and significantly enhancing the system's practical security. Using transmit-receive beamforming techniques, the system transforms MIMO channels into multiple parallel lossy quantum channels, enabling robust key distribution between Alice and Bob. This study examines entanglement-based and prepare-and-measure protocols, deriving secret key rates for both asymptotic and finite code scenarios. Simulations reveal the critical role of multiple antenna configurations and efficient homodyne detection in mitigating free-space path loss and maximizing key rates. Results indicate that system performance is optimized at lower THz frequencies for long-range transmissions and higher frequencies for short-range applications. The proposed protocol offers a scalable solution for secure quantum communications in next-generation wireless networks, demonstrating potential for deployment in both indoor and outdoor environments.

quant-pharXiv:2511.05021•IEEE Transactions on Vehicular Technology•Nov 10, 2025•0 citations

Millimetre-waves to Terahertz SISO and MIMO Continuous Variable Quantum Key Distribution

Mingqi Zhang, Stefano Pirandola, Kaveh Delfanazari

With the exponentially increased demands for large bandwidth, it is important to think about the best network platform as well as the security and privacy of the information in communication networks. Millimetre (mm)-waves and terahertz (THz) with high carrier frequency are proposed as the enabling technologies to overcome Shannons channel capacity limit of existing communication systems by providing ultrawide bandwidth signals. Mm-waves and THz are also able to build wireless links compatible with optical communication systems. However, most solid-state components that can operate reasonably efficiently at these frequency ranges (100GHz-10THz), especially sources and detectors, require cryogenic cooling, as is a requirement for most quantum systems. Here, we show that secure mm-waves and THz QKD can be achieved when the sources and detectors operate at cryogenic temperatures down to T= 4K. We compare single-input single-output (SISO) and multiple-input multiple-output (MIMO) Continuous Variable THz Quantum Key Distribution (CVQKD) schemes and find the positive secret key rate in the frequency ranges between f=100 GHz and 1 THz. Moreover, we find that the maximum transmission distance could be extended, the secret key rate could be improved in lower temperatures, and achieve a maximum secrete communication distance of more than 5 km at f=100GHz and T=4K by using 1024*1024 antennas. Our results may contribute to the efforts to develop next-generation secure wireless communication systems and quantum internet for applications from inter-satellite and deep space, to indoor and short-distance communications.

arXiv:2301.04723•Jan 11, 2023•1 citation

Millimeter-Waves to Terahertz SISO and MIMO Continuous Variable Quantum Key Distribution

Mingqi Zhang, Stefano Pirandola, Kaveh Delfanazari

With the exponentially increased demands for large bandwidth, it is important to think about the best network platform as well as the security and privacy of the information in communication networks. Millimetre (mm)-waves and terahertz (THz) with high carrier frequency are proposed as the enabling technologies to overcome Shannon's channel capacity limit of existing communication systems by providing ultrawide bandwidth signals. Mm-waves and THz are also able to build wireless links compatible with optical communication systems. However, most solid-state components that can operate reasonably efficiently at these frequency ranges (100GHz-10THz), especially sources and detectors, require cryogenic cooling, as is a requirement for most quantum systems. Here, we show that secure mm-waves and THz QKD can be achieved when the sources and detectors operate at cryogenic temperatures down toT= 4K. We compare single-input single-output (SISO) and multiple-input multiple-output (MIMO) Continuous Variable THz Quantum Key Distribution (CVQKD) schemes and find the positive secret key rate in the frequency ranges betweenf=100 GHz and 1 THz. Moreover, we find that the maximum transmission distance could be extended, the secret key rate could be improved in lower temperatures, and achieve a maximum secrete communication distance of more than 5km atf=100GHz andT=4K by using 1024×1024 antennas. Our results for the first time show the possibility of mm-waves and THz MIMO CVQKD with the system operating at temperatures belowT= 50K, which may contribute to the efforts to develop next-generation secure wireless communication systems and quantum internet for applications from inter-satellite and deep space to indoor and short-distance communications.

IEEE Transactions on Quantum Engineering•Jan 1, 2023•26 citations

MIMO Terahertz Quantum Key Distribution

Neel Kanth Kundu, Dash, SP, Matthew R. McKay +1 more

We propose a multiple-input multiple-output (MIMO) quantum key distribution (QKD) scheme for terahertz (THz) frequency applications operating at room temperature. Motivated by classical MIMO communications, a transmit-receive beamforming scheme is proposed that converts the rank-$r$ MIMO channel between Alice and Bob into $r$ parallel lossy quantum channels. Compared with existing single-antenna QKD schemes, we demonstrate that the MIMO QKD scheme leads to performance improvements by increasing the secret key rate and extending the transmission distance. Our simulation results show that multiple antennas are necessary to overcome the high free-space path loss at THz frequencies. We demonstrate a non-monotonic relation between performance and frequency, and reveal that positive key rates are achievable in the 10–30 THz frequency range. The proposed scheme can be used for both indoor and outdoor QKD applications for beyond fifth generation ultra-secure wireless communications systems.

•Oct 1, 2021•47 citations

MIMO Terahertz Quantum Key Distribution

Neel Kanth Kundu, Soumya Prakash Dash, Matthew R. McKay +1 more

We propose a multiple-input multiple-output (MIMO) quantum key distribution (QKD) scheme for terahertz (THz) frequency applications operating at room temperature. Motivated by classical MIMO communications, a transmit-receive beamforming scheme is proposed that converts the rank-$r$MIMO channel between Alice and Bob into$r$parallel lossy quantum channels. Compared with existing single-antenna QKD schemes, we demonstrate that the MIMO QKD scheme leads to performance improvements by increasing the secret key rate and extending the transmission distance. Our simulation results show that multiple antennas are necessary to overcome the high free-space path loss at THz frequencies. We demonstrate a non-monotonic relation between performance and frequency, and reveal that positive key rates are achievable in the 10–30 THz frequency range. The proposed scheme can be used for both indoor and outdoor QKD applications for beyond fifth generation ultra-secure wireless communications systems.

arXiv:2105.03642•IEEE Communications Letters•Aug 5, 2021•0 citations

Secret Key Rate Analysis of RIS-Assisted THz MIMO CV-QKD Systems under Access-Constrained Eavesdropping

Sushil Kumar, Soumya Prakash Dash, George C. Alexandropoulos

A reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) continuous-variable quantum key distribution (CV-QKD) system operating at terahertz (THz) frequencies, in which a transmitter, Alice, encodes secret keys using Gaussian-modulated coherent states and communicates them to a legitimate receiver, Bob, is considered in this paper. The composite wireless channel, comprising the direct Alice-Bob link and the RIS-assisted reflected link, is modeled as a passive linear Gaussian quantum channel, enabling a unitary dilation that preserves the canonical commutation relations. The security of the considered system is investigated under collective Gaussian entangling attacks by introducing a practical access-constrained eavesdropping model, in which an eavesdropper, Eve, is assumed to access only the environmental modes associated with physically accessible propagation segments. A unified analytical framework is developed to derive the achievable secret key rate (SKR) across all single-segment, pairwise-segment, and full-segment access scenarios, assuming homodyne detection and reverse reconciliation at Bob. Furthermore, an optimization framework is developed to determine the optimal RIS phase configuration matrix and transmitter/receiver beam-splitter parameters that maximize the SKR performance. The resulting optimization problem is efficiently solved using particle swarm optimization. Numerical results are presented to demonstrate the system's performance with respect to various free parameters. It is showcased that the secrecy performance strongly depends on Eve's accessible propagation segments, with the Alice-RIS channel constituting the most security-critical segment.

arXiv:2603.28252•Mar 30, 2026•0 citations
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.
Although multiple-input multiple-output (MIMO) terahertz (THz) continuous-variable quantum key distribution (CVQKD) is theoretically secure, practical vulnerabilities may arise due to detector imperfections. This paper explores a CV measurement-device-independent (MDI) QKD system operating at THz frequencies within a MIMO framework. In this system, measurement is delegated to an untrusted third party, Charlie, rather than the receiver, eliminating all detector attacks and significantly enhancing the system's practical security. Using transmit-receive beamforming techniques, the system transforms MIMO channels into multiple parallel lossy quantum channels, enabling robust key distribution between Alice and Bob. This study examines entanglement-based and prepare-and-measure protocols, deriving secret key rates for both asymptotic and finite code scenarios. Simulations reveal the critical role of multiple antenna configurations and efficient homodyne detection in mitigating free-space path loss and maximizing key rates. Results indicate that system performance is optimized at lower THz frequencies for long-range transmissions and higher frequencies for short-range applications. The proposed protocol offers a scalable solution for secure quantum communications in next-generation wireless networks, demonstrating potential for deployment in both indoor and outdoor environments.
With the exponentially increased demands for large bandwidth, it is important to think about the best network platform as well as the security and privacy of the information in communication networks. Millimetre (mm)-waves and terahertz (THz) with high carrier frequency are proposed as the enabling technologies to overcome Shannons channel capacity limit of existing communication systems by providing ultrawide bandwidth signals. Mm-waves and THz are also able to build wireless links compatible with optical communication systems. However, most solid-state components that can operate reasonably efficiently at these frequency ranges (100GHz-10THz), especially sources and detectors, require cryogenic cooling, as is a requirement for most quantum systems. Here, we show that secure mm-waves and THz QKD can be achieved when the sources and detectors operate at cryogenic temperatures down to T= 4K. We compare single-input single-output (SISO) and multiple-input multiple-output (MIMO) Continuous Variable THz Quantum Key Distribution (CVQKD) schemes and find the positive secret key rate in the frequency ranges between f=100 GHz and 1 THz. Moreover, we find that the maximum transmission distance could be extended, the secret key rate could be improved in lower temperatures, and achieve a maximum secrete communication distance of more than 5 km at f=100GHz and T=4K by using 1024*1024 antennas. Our results may contribute to the efforts to develop next-generation secure wireless communication systems and quantum internet for applications from inter-satellite and deep space, to indoor and short-distance communications.
With the exponentially increased demands for large bandwidth, it is important to think about the best network platform as well as the security and privacy of the information in communication networks. Millimetre (mm)-waves and terahertz (THz) with high carrier frequency are proposed as the enabling technologies to overcome Shannon's channel capacity limit of existing communication systems by providing ultrawide bandwidth signals. Mm-waves and THz are also able to build wireless links compatible with optical communication systems. However, most solid-state components that can operate reasonably efficiently at these frequency ranges (100GHz-10THz), especially sources and detectors, require cryogenic cooling, as is a requirement for most quantum systems. Here, we show that secure mm-waves and THz QKD can be achieved when the sources and detectors operate at cryogenic temperatures down toT= 4K. We compare single-input single-output (SISO) and multiple-input multiple-output (MIMO) Continuous Variable THz Quantum Key Distribution (CVQKD) schemes and find the positive secret key rate in the frequency ranges betweenf=100 GHz and 1 THz. Moreover, we find that the maximum transmission distance could be extended, the secret key rate could be improved in lower temperatures, and achieve a maximum secrete communication distance of more than 5km atf=100GHz andT=4K by using 1024×1024 antennas. Our results for the first time show the possibility of mm-waves and THz MIMO CVQKD with the system operating at temperatures belowT= 50K, which may contribute to the efforts to develop next-generation secure wireless communication systems and quantum internet for applications from inter-satellite and deep space to indoor and short-distance communications.
We propose a multiple-input multiple-output (MIMO) quantum key distribution (QKD) scheme for terahertz (THz) frequency applications operating at room temperature. Motivated by classical MIMO communications, a transmit-receive beamforming scheme is proposed that converts the rank-rrr MIMO channel between Alice and Bob into rrr parallel lossy quantum channels. Compared with existing single-antenna QKD schemes, we demonstrate that the MIMO QKD scheme leads to performance improvements by increasing the secret key rate and extending the transmission distance. Our simulation results show that multiple antennas are necessary to overcome the high free-space path loss at THz frequencies. We demonstrate a non-monotonic relation between performance and frequency, and reveal that positive key rates are achievable in the 10–30 THz frequency range. The proposed scheme can be used for both indoor and outdoor QKD applications for beyond fifth generation ultra-secure wireless communications systems.
We propose a multiple-input multiple-output (MIMO) quantum key distribution (QKD) scheme for terahertz (THz) frequency applications operating at room temperature. Motivated by classical MIMO communications, a transmit-receive beamforming scheme is proposed that converts the rank-rrrMIMO channel between Alice and Bob intorrrparallel lossy quantum channels. Compared with existing single-antenna QKD schemes, we demonstrate that the MIMO QKD scheme leads to performance improvements by increasing the secret key rate and extending the transmission distance. Our simulation results show that multiple antennas are necessary to overcome the high free-space path loss at THz frequencies. We demonstrate a non-monotonic relation between performance and frequency, and reveal that positive key rates are achievable in the 10–30 THz frequency range. The proposed scheme can be used for both indoor and outdoor QKD applications for beyond fifth generation ultra-secure wireless communications systems.
A reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) continuous-variable quantum key distribution (CV-QKD) system operating at terahertz (THz) frequencies, in which a transmitter, Alice, encodes secret keys using Gaussian-modulated coherent states and communicates them to a legitimate receiver, Bob, is considered in this paper. The composite wireless channel, comprising the direct Alice-Bob link and the RIS-assisted reflected link, is modeled as a passive linear Gaussian quantum channel, enabling a unitary dilation that preserves the canonical commutation relations. The security of the considered system is investigated under collective Gaussian entangling attacks by introducing a practical access-constrained eavesdropping model, in which an eavesdropper, Eve, is assumed to access only the environmental modes associated with physically accessible propagation segments. A unified analytical framework is developed to derive the achievable secret key rate (SKR) across all single-segment, pairwise-segment, and full-segment access scenarios, assuming homodyne detection and reverse reconciliation at Bob. Furthermore, an optimization framework is developed to determine the optimal RIS phase configuration matrix and transmitter/receiver beam-splitter parameters that maximize the SKR performance. The resulting optimization problem is efficiently solved using particle swarm optimization. Numerical results are presented to demonstrate the system's performance with respect to various free parameters. It is showcased that the secrecy performance strongly depends on Eve's accessible propagation segments, with the Alice-RIS channel constituting the most security-critical segment.