How does Earth’s spacetime deformation affect quantum communications?

Jan Kohlrus investigates relativitic effects to consider when setting up quantum communication systems.

Jan Kohlrus

This is a guest post by Jan Kohlrus

The interplay and overlap between relativity and quantum theory are among the most complex and challenging open problems of modern theoretical physics. This grey area has been extensively studied on the theoretical side, sometimes following very speculative and exotic directions, while very few experiments have been proposed in a way that rigorously incorporates relativity and quantum features.

The purpose of our work is to propose feasible experiments that involve quantum fields in a relativistic framework. In our recent article in EPJ Quantum Technology, we study how observers that undergo different motion, and experience different strengths of the gravitational field, measure pulses of light that propagate from one user to another. In particular, we look at quantum communication schemes between Earth and satellite links, as well as between two satellites.

We start by considering the deformation of the spacetime due to the presence of the Earth and its rotation, as predicted by general relativity. We model the background by the Kerr metric. This curved background alters the shape and nature of pulses of light that propagate from a link to another. This change is directly related to the gravitational frequency shift of the photons exchanged between these observers.

We employ modern techniques from the field of quantum metrology to compare the state of the photons that has been sent with the one that is received, and provide the errors introduced when attempting to measure selected parameters. In the first case, we give quantitative predictions on how curved spacetime and the motion of observers affect simple quantum key distribution (QKD) and quantum communication protocols. In the other, we find the ultimate bounds on measurements of the Schwarzschild radius of the Earth, which is a quantity directly related to the Earth’s mass.

In this work, we have been able to account for the rotation of the Earth, the velocity of the observers (i.e., special relativistic effects), and we have studied satellite-to-satellite communication schemes. These improvements have greatly increased our capability of investigating physics within space-based scenarios. Our extended framework brought forward new insights, which we list below:

  • First we find that quantum communications and quantum metrology applied to static parameters of the Earth (i.e., its mass) are very robust against the dragging effects of Earth’s rotation;
  • Secondly, we find that satellite-to-satellite schemes give better results when performing quantum measurements of the mass of the Earth, while Earth-to-satellite setups perform much better when measuring rotation parameters of the Earth, such as its equatorial angular velocity;
  • Finally, inclusions of special relativistic effects led us to discover a class of circular orbits for which quantum communications between an observer on Earth and a satellite are almost not affected by the curved spacetime background. This can potentially provide us with a good reference channel.

To conclude, we believe that these physical insights and quantitative predictions will aid the development of space-based quantum communications and quantum experiments, therefore leading to a better understanding of the interplay between relativistic effects and quantum physics.

Read the full article here.


Jan Kohlrus studied physics at the University of Paris-Sud and obtained his master in mathematical and theoretical physics at the University of Aix-Marseille. He is a PhD candidate at the University of Nottingham in the group Relativistic Quantum Technologies of Ivette Fuentes.


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