Wootters’s concurrence is a physical quantity that quantitatively describes the degree of entanglement of two qubit states. The concurrence of spatial entangled two-qubit states produced by spontaneous parametric down transform in turbulent adsorbent seawater is presented. The Kolmogorov ocean spectrum and structural constants of the salinity-temperature fluctuation are presented, which can simplify the complexity of the study of the turbulence effects of light wave transport in weakly turbulent oceans. The optimization parameters of the information source system corresponding to the transmission rate of high concurrence are also explored. The results show that the parameters of the spontaneous parametric down transform will make a great impact on the concurrence. The smaller interval between the two signal apertures and the interval between the signal and the idle apertures will make the communication system have higher transmission fidelity of the concurrence. The concurrence can maintain higher in the oceanic turbulence with small the rate of dissipation of mean-square temperature and large rate of dissipation of kinetic energy per unit mass of fluid. These results are of great significance for the design of an underwater optical quantum communication system with optimal concurrence transmission.
Wootters’s concurrence is a physical quantity that quantitatively describes the degree of entanglement of two qubit states. The concurrence of spatial entangled two-qubit states produced by spontaneous parametric down transform in turbulent adsorbent seawater is presented. The Kolmogorov ocean spectrum and structural constants of the salinity-temperature fluctuation are presented, which can simplify the complexity of the study of the turbulence effects of light wave transport in weakly turbulent oceans. The optimization parameters of the information source system corresponding to the transmission rate of high concurrence are also explored. The results show that the parameters of the spontaneous parametric down transform will make a great impact on the concurrence. The smaller interval between the two signal apertures and the interval between the signal and the idle apertures will make the communication system have higher transmission fidelity of the concurrence. The concurrence can maintain higher in the oceanic turbulence with small the rate of dissipation of mean-square temperature and large rate of dissipation of kinetic energy per unit mass of fluid. These results are of great significance for the design of an underwater optical quantum communication system with optimal concurrence transmission.
The effect of the turbulent motion of ocean on the quantum communication based on the orbital angular momentum in an underwater quantum channel is studied in this work. Based on the power spectrum model of ocean turbulence proposed by Elamassie, the quantitative relationships of different ocean turbulence parameters with the single photon detection probability of orbital angular momentum photons, the channel capacity, the key generation rate, the concurrence of two entangled photons are proposed. The maximum entanglement distance of the orbital angular momentum entangled photon-pairs in the ocean turbulence is further studied by the universal entanglement decay of the concurrence of entangled photon-pairs in the ocean turbulence. The results show that the detection probability of single photon, the channel capacity, the key generation rate, and the concurrence of entangled photon-pairs decrease with the increase of the dissipation rate of turbulent kinetic energy and the decrease of the rate of dissipation of mean-squared temperature. The influence of the temperature and salinity balance parameter of ocean turbulence on the performance of underwater quantum communication are significantly different under the condition of whether the stable stratification of seawater is assumed or not. In the ocean turbulent environment, the increasing of the initial orbital angular momentum quantum number of signal photons can improve the key generation rate of quantum key distribution and the resistance of entangled photons to entanglement decay.
We study the effects of atmospheric turbulence on the entanglement of spatial two-qubit states that are prepared using the signal and idler photons produced by parametric down-conversion. Such states are the basic ingredients of quantum information protocols and can be prepared, for example, by making down-converted photons pass through a pair of double-apertures. We make use of the Kolmogorov model for atmospheric turbulence and quantify the entanglement of the two-qubit state in terms of Wootters's concurrence. We restrict our analysis to the two-qubit states that can be represented by density matrices having only two nonzero diagonal elements.
The propagation properties of Laguerre-Gaussian beams in oceanic turbulence are investigated for both single-photon and biphoton cases. For single-photon communication, the channel capacity and trace distance are employed, both of which effectively reveal the communication performance via different viewpoints. For the biphoton case, we consider distributions of quantum resources including entanglement and quantum coherence. Turbulence conditions with a larger inner-scale and anisotropic factors, higher dissipation rate of kinetic energy, lower dissipation rate of the mean-squared temperature, and lower temperature-salinity contribution ratio combined with longer wavelength and an appropriate range of optimal beam width are beneficial to communication performances. Our results provide theoretical significance to improve the orbital-angular-momentum communication via oceanic turbulence.
Quantum key distribution (QKD) has been identified as a viable solution for secure underwater communication. This study aims to characterize the impact of natural turbulent waters on systems. The performance of QKD systems is analyzed in terms of the quantum bit error rate and the secret key rate. We expand upon previous studies which only considered large separations by including large and small separations by comparing the turbulence length scale with the distance between two observation points. To that end, we obtain the analytical expression of the wave structure function (WSF) for small separation for propagating Gaussian beams. Since the WSF describes how the amplitude and phase of an optical wave change as it travels through the varying refractive index of the turbulent medium over a given distance, the accurate characterization remains essential in terms of revealing the beam wavefront distortion. Leveraging the practical parameters of underwater environment and communication systems, we demonstrate that the average temperature, average salinity concentration, temperature-salinity gradient, temperature and energy dissipation rates of turbulent water impact the performance and security of the QKD systems to a nonnegligible extent. It is also observed that the waters having high chlorophyll concentrations, e.g., coastal waters, drastically decrease the performance of the QKD systems due to strong absorption and scattering effects. The findings and insights gained from this study may help advance secure underwater communication, which in turn will aid in establishing future QKD networks. Potential applications of this research include secure underwater communication for defense, data gathering for marine environmental monitoring, remote data transmission, and deep-sea exploration.
We employ non-diffractive Bessel-Gaussian beams to investigate the effect of oceanic turbulence on quantum communication protocols via behaviors of quantum-channel capacity and trace distance, based on the analytical expression of the phase structure function of an orbital-angular-momentum (OAM) beam in underwater wireless optical communication. Our results show that turbulence conditions with a larger inner-scale and outer-scale factors, higher dissipation rate of kinetic energy, lower dissipation rate of the mean-squared temperature, and smaller temperature-salinity contribution ratio are beneficial to quantum communication performance. Moreover, we show that the distribution protocol may be improved by distributing quantum superposition states instead of OAM eigenstates. We believe our work provides the first theoretical exploration of quantum-channel capacity in underwater OAM quantum communication.
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.