A continuous-variable quantum key distribution (CVQKD) can be realized over the seawater channel, but the transmission of quantum signals in seawater media exhibits significant attenuation effects. Therefore, we propose an N-symbol amplitude and phase shift keying (N-APSK) modulation scheme to enhance the transmission performance of the CVQKD over the seawater channel. Specifically, an optimal N-APSK modulation scheme is designed based on the principle of maximizing the minimum Euclidean distance (MED). The simulation results show that the CVQKD protocol based on N-APSK modulation achieves a longer transmission distance over the seawater channel compared to the Gaussian modulation protocol. Additionally, increasing the value of N simultaneously expands the number of rings in the constellation diagram, further enhancing the communication distance. This study transfers modulation methods from the field of classical communications to the field of quantum communications, achieving a substantial improvement in communication distance and thereby promoting the integration of quantum communications and classical communications.
A continuous-variable quantum key distribution (CVQKD) can be realized over the seawater channel, but the transmission of quantum signals in seawater media exhibits significant attenuation effects. Therefore, we propose an N-symbol amplitude and phase shift keying (N-APSK) modulation scheme to enhance the transmission performance of the CVQKD over the seawater channel. Specifically, an optimal N-APSK modulation scheme is designed based on the principle of maximizing the minimum Euclidean distance (MED). The simulation results show that the CVQKD protocol based on N-APSK modulation achieves a longer transmission distance over the seawater channel compared to the Gaussian modulation protocol. Additionally, increasing the value of N simultaneously expands the number of rings in the constellation diagram, further enhancing the communication distance. This study transfers modulation methods from the field of classical communications to the field of quantum communications, achieving a substantial improvement in communication distance and thereby promoting the integration of quantum communications and classical communications.
The trans-media transmission of quantum pulse is one of means of free-space transmission which can be applied in continuous-variable quantum key distribution (CVQKD) system. In traditional implementations for atmospheric channels, the 1500-to-1600-nm pulse is regarded as an ideal quantum pulse carrier. However, the underwater transmission of this pulses tends to suffer from severe attenuation, which inevitably deteriorates the security of the whole CVQKD system. In this paper, we propose an alternative scheme for implementations of CVQKD over satellite-to-submarine channels. We estimate the parameters of the trans-media channels, involving atmosphere, sea surface and seawater and find that the short-wave infrared performs well in the above channels. The 450-nm pulse is used for generations of quantum signal carriers to accomplish quantum communications through atmosphere, sea surface and seawater channels. Numerical simulations show that the proposed scheme can achieve the transmission distance of 600 km. In addition, we demonstrate that non-Gaussian operations can further lengthen its maximal transmission distance, which contributes to the establishment of practical global quantum networks.
Continuous variable quantum key distribution (CVQKD) can be potentially implemented through seawater channels, whereas the involved oceanic turbulence has a negative effect on the maximal transmission distance of quantum communication systems. Here, we demonstrate the effects of the oceanic turbulence on the performance of the CVQKD system and suggest an implementation feasibility of the passive CVQKD through the oceanic turbulence-based channel. We achieve the channel transmittance characterized by the transmission distance and depth of the seawater. Moreover, a non-Gaussian approach is used for performance improvement while counteracting the effects of excess noises on the oceanic channel. Numerical simulations show that the photon operation (PO) unit can bring reductions of excess noise when taking into account the oceanic turbulence, and hence results in performance improvement in terms of transmission distance and depth as well. The passive CVQKD explores the intrinsic field fluctuations of a thermal source without using an active scheme and hence has a promising application in chip integration for portable quantum communications.
Abstract Continuous-variable quantum secure direct communication (CVQSDC) with Gaussian modulation (GM) demands a considerable quantity of random numbers during the preparation process and encodes them separately on the quadrature components of the quantum states. Hence, high-speed random number generators are required to satisfy this demand, which is difficult to implement in practical applications. CVQSDC with discrete modulation (DM), correspondingly, employs a finite number of quantum states to achieve encoding, which can circumvent the shortcomings of the GM scheme. Based on the advantages of DM, the issue of attaining the most optimal secrecy capacity and communication distance remains to be resolved. Here, we propose a CVQSDC protocol based on N-symbol amplitude phase shift keying (N-APSK), which exploits the Boltzmann–Maxwell distribution assisted probability shaping technique. In comparison with the uniform distribution, according to 32-APSK CVQSDC, the proposed scheme extends the communication distance by about 38%, while obtaining a higher secrecy capacity at the same communication distance. Furthermore, increasing the value of N will concurrently increase the quantity of rings in the constellation, thereby facilitating enhancements of communication distance. This work incorporates the modulation approaches prevalently employed in classical communication into the realm of quantum communication, attaining gratifying advancements in communication distance and secrecy capacity, and concurrently facilitating the integrated development of quantum communication and classical communication.
Discrete modulation continuous variable quantum key distribution (DM-CV-QKD) is highly considered in real implementations to avoid the complexity of Gaussian modulation (GM), which is optimum in terms of the key rate. DM-CV-QKD systems usually consider M-symbol phase shift keying (M-PSK) constellations. However, this type of constellation cannot reach transmission distances and key rates as high as GM, limiting the practical implementation of CV-QKD systems. Here, by considering M-symbol amplitude and phase shift keying (M-APSK) constellations, we can approximate GM. Indeed, considering finite-size effects, 4 ring 64-APSK can reach 52.0 km, only 7.2 km less than GM and 282% the maximum achievable transmission distance for 8-PSK.
Continuous-Variable Quantum Key Distribution (CVQKD), based on quantum mechanical principles, offers theoretically unconditional security and represents a crucial direction for future secure communications. However, its application in marine environments faces challenges such as high attenuation, scattering, and turbulence in seawater, severely impacting quantum signal transmission and secure key generation efficiency. Orbital angular momentum (OAM) multiplexing technology leverages the orthogonality of photon OAM modes to transmit multiple independent quantum signals in parallel within a single spatial channel. In this scheme, each OAM mode serves as an independent sub-channel, enabling simultaneous key distribution across multiple modes, thereby significantly enhancing the system’s secure key rate and spectral efficiency. This paper proposes an OAM-multiplexed CVQKD scheme tailored for marine channels. Based on Yi’s power spectrum model for marine turbulence refractive index fluctuations, we derive expressions for OAM mode probability density and detection probability. Through system modeling and performance analysis, we investigate the impact of marine turbulence on OAM modes, as well as on the secure key rate and transmission distance of CVQKD systems. Results indicate that higher-order OAM modes exhibit more pronounced turbulence effects, leading to reduced key rates and limited transmission distances. The OAM multiplexing approach significantly enhances system key rates, providing theoretical and technical references for constructing high-rate seawater quantum communication networks.
We propose a continuous-variable quantum key distribution (CVQKD) scheme based on the atmosphere-to-seawater channel. In particular, an untrusted entanglement source (two modes of the compressed vacuum state, TMSV) is deployed on the surface of the seawater, each mode of TMSV is sent to one of the two legitimate parts, respectively. In this way, we can establish a trans-media CVQKD link between the atmosphere and the underwater. Meanwhile, a suitable non-Gaussian operation, namely photon subtraction, is introduced to enhance the performance of the trans-media CVQKD scheme. Security analysis shows that the proposed scheme can establish a trans-media quantum communication system on the atmosphere-to-seawater channel. Moreover, the maximum transmission distance can be further extended by using proper photon subtraction operation. Our scheme provides a guidance for applying CVQKD to trans-media channels.