Satellite-based continuous-variable quantum key distribution under the Earth's gravitational field

TL;DR

This paper investigates how Earth's gravitational field affects continuous-variable quantum key distribution (CV-QKD) from satellites, revealing gravitational erosion of key rates and potential strategies to mitigate this loss by adjusting satellite orbits.

Contribution

It introduces a general method to analyze gravitational effects on CV-QKD and uncovers the non-monotonic behavior of key rates with satellite height, including a quantification of gravitational frequency shift impacts.

Findings

Gravitational field erodes QKD key rates at all satellite heights.

Key rates initially increase around half the Earth's radius before decreasing with higher orbits.

Gravitational frequency shift effects can be measured within 1% at geostationary orbits.

Abstract

Long distance communication protocols cannot ignore the existence of the Earth's gravitational field and its effects on quantum states. In this work, we show a very general method to consider the effects of the Earth's gravitational field on continuous-variable quantum key distribution protocols. Our results show that the Earth's gravitational field erodes the ability of the two parties to perform QKD in all the protocols. However, our findings also exhibit some interesting features, i.e., the key rates initially increase for a specific range of height parameter $h\simeq r_A/2$ and then gradually decrease with the increasing of the orbits of satellite $h$. A possible explanation is also provided in our analysis, considering the fact that gravitational frequency shift and special relativistic effects play different roles in the key rates. In addition, our findings show that the change in key rate effected by gravitational frequency shift can be determined at a level of $<1.0\%$ within the satellite height at geostationary Earth orbits. Our work could provide some interesting possibilities to reduce the loss key rate through the control of the orbital height of satellites.