Quantum key distribution (QKD) has undergone significant development in recent decades, particularly with respect to free-space (air) and optical fiber channels. Here, we report the first proof-ofprinciple experiment for the BB84 protocol QKD over a water channel. Firstly, we demonstrate again the polarization preservation properties of the water channel in optical transmission according to the measured Mueller matrix, which is close to the unit matrix. The reason for the polarization preservation, revealed by Monte Carlo simulation, is that almost all the received photons are unscattered.Then, we performed the first polarization encoding BB84 protocol QKD over a 2.37m water channel. The results show that QKD can be performed with a low quantum bit error rate (QBER), less than 3.5%, with different attenuation coefficients.
Underwater quantum key distribution (QKD) has potential applications in absolutely secure underwater communication. However, the performance of underwater QKD is limited by the optical elements, background light, and dark counts of the detector. In this paper, we propose a modified formula for the quantum bit error rate (QBER), which takes into account the effect of detector efficiency on the QBER caused by the background light. Then we calculate the QBER of the polarization encoding BB84 protocol in Jerlov type seawater by analyzing the effect of the background light and optical components in a more realistic situation. Finally, we further analyze the final key rate and the maximum secure communication distance in three propagation modes, i.e., upward, downward and horizontal modes. We find that secure QKD can be performed in the clearest Jerlov type seawater at a distance of hundreds of meters, even in the worst downward propagation mode. Specifically, by optimizing the system parameters, it is possible to securely transmit information with a rate of 67kbits/s at a distance of 100 m in the seawater channel with an attenuation coefficient of 0.03/m at night. For practical underwater QKD, the performance can also be improved by using decoy states. Our results are useful to long distance underwater quantum communication.
Quantum steering, a type of quantum correlation with unique asymmetry, has important applications in asymmetric quantum information tasks. We consider a new quantum steering scenario in which one half of a two-qubit Werner state is sequentially measured by multiple Alices and the other half by multiple Bobs. We find that the maximum number of Alices who can share steering with a single Bob increases from 2 to 5 when the number of measurement settings N increases from 2 to 16. Furthermore, we find a counterintuitive phenomenon that for a fixed N, at most 2 Alices can share steering with 2 Bobs, while 4 or more Alices are allowed to share steering with a single Bob. We further analyze the robustness of the steering sharing by calculating the required purity of the initial Werner state, the lower bound of which varies from 0.503(1) to 0.979(5). Finally, we show that our both-sides sequential steering sharing scheme can be applied to control the steering ability, even the steering direction, if an initial asymmetric state or asymmetric measurement is adopted. Our work gives insights into the diversity of steering sharing and can be extended to study the problems such as genuine multipartite quantum steering when the sequential unsharp measurement is applied.
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