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arXiv:1807.11855 · Physical review. D/Physical review. D.

Effects of gravity on continuous-variable quantum key distribution

Roberto Pierini

Published Dec 13, 2018• 9 citations
arXivHTMLPDF

Abstract

The domain of quantum technologies has been recently broadened to satellites orbiting the Earth. Long distance communication protocols cannot ignore the presence of the gravitational field and the effects on the quantum states. Here, we provide a general method to investigate how noninertial motion affects the performance of various quantum key distribution protocols for continuous-variable states of localized wave packets. Taking advantage of the equivalence principle, our results can be thought of as due to the gravitational field. We show that the consequences of gravity strongly depend on the configuration and the cryptographic scheme used.

DOI
10.1103/physrevd.98.125007

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The domain of quantum technologies has been recently broadened to satellites orbiting the Earth. Long distance communication protocols cannot ignore the presence of the gravitational field and the effects on the quantum states. Here, we provide a general method to investigate how noninertial motion affects the performance of various quantum key distribution protocols for continuous-variable states of localized wave packets. Taking advantage of the equivalence principle, our results can be thought of as due to the gravitational field. We show that the consequences of gravity strongly depend on the configuration and the cryptographic scheme used.
Continuous-variable quantum key distribution has gradually shifted from optical fiber communication to space communication. In free-space quantum communication, the influence of gravity cannot be ignored. In light of the influence of gravity, this study assesses the efficacy of the thermal-state continuous-variable quantum key distribution (QKD) protocol in a non-inertial reference frame. This differs from the conventional scenario in an inertial reference frame, where pure vacuum Gaussian states are employed without consideration of the influence of gravity. This study examines the potential and challenges of quantum key distribution in the presence of gravitational effects. The feasibility of generating the key under the influence of gravity through the lens of quantum state transfer in a non-inertial reference system is also analyzed. It presents a comprehensive mathematical derivation and simulation of the secret key rate for maintaining a positive rate under specific conditions. Furthermore, it presents a detailed implementation plan for thermal-state quantum key distribution in a non-inertial reference frame, particularly in the context of gravity. It offers valuable insights into the performance of quantum communication in unconventional settings.
ABSTRACT Quantum communication is gradually shifting from terrestrial fiber‐optic communication to satellite‐based space communication. The impact of gravitational fields on quantum states in quantum communication protocols cannot be overlooked. In this paper, a general method to investigate how non‐inertial motion affects multiparty quantum communication is proposed. Specifically, we examine the influence of non‐inertial motion on the performance of the protocol based on measurement‐device‐independent multiparty quantum communication using continuous‐variable Greenberger–Horne–Zeilinger (CV GHZ) states. Our results demonstrate that the choice of system configuration and cryptographic scheme largely determines the effects of gravitational fields.
The influence of gravity on quantum key distribution cannot be ignored in practical space communication. This paper provides a thorough analysis of the effectiveness of gravity on continuous-variable quantum key distribution with discrete-modulated states. By calculating the acceleration in both inertial and non-inertial reference systems based on the discrete variable variance calculation formula, the gain coefficient is obtained. Based on this parameter, an improved protocol with a high key rate over a spatial transmission distance of 390 km is proposed, enabling the practical application of quantum key distribution techniques. The results can be used to demonstrate the performance of continuous-variable quantum key distribution with discrete modulation influenced by gravity. This paper not only extends the range of discrete modulation states, but also enhances the impact of relativistic quantum information.
Space-based quantum communication naturally involves satellites and ground stations exchanging optical signals at high altitudes and large relative velocities. Starting from general relativistic considerations, we systematically separate the frequency shift into longitudinal Doppler contributions, relativistic corrections, and corrections from the propagation delay (retardation). We find the relativistic corrections to the Keplerian satellite orbits to be negligible on the considered timescale, compared to the gravitational and special relativistic time dilation contributions to the frequency shift. Somewhat surprisingly, we find the contribution from the retardation effect to be on the same order of magnitude as the relativistic contributions. To analyze the significance of these effects, we investigate secret key capacities for a continuous variable quantum key distribution protocol for various configurations of satellite orbits and ground stations. We find that the corrections from relativistic effects and retardation significantly impact the communication performance and should be taken into account.
Efficiencies of quantum information protocols can be affected by the noninertial motion of involved parties, e.g., in a gravitational field. Most of the previous studies focused on the effects of such a motion on a bipartite entanglement as a resource. We show how a tripartite Gaussian resource state of continuous variables is affected by the acceleration of the observers. Specifically, we analyze how genuine tripartite entanglement degrades due to the motion for various initial states and trajectories of the involved parties.