Abstract
The current race in quantum communication – endeavouring to establish a global quantum network – must account for special and general relativistic effects. The well-studied general relativistic effects include Shapiro time-delay, gravitational lensing, and frame dragging which all are due to how a mass distribution alters geodesics. Here, we report how the curvature of spacetime geometry affects the propagation of information carriers along an arbitrary geodesic. An explicit expression for the distortion onto the carrier wavefunction in terms of the Riemann curvature is obtained. Furthermore, we investigate this distortion for anti de Sitter and Schwarzschild geometries. For instance, the spacetime curvature causes a 0.10 radian phase-shift for communication between Earth and the International Space Station on a monochromatic laser beam and quadrupole astigmatism; can cause a 12.2% cross-talk between structured modes traversing through the solar system. Our finding shows that this gravitational distortion is significant, and it needs to be either pre- or post-corrected at the sender or receiver to retrieve the information.
Highlights
The current race in quantum communication – endeavouring to establish a global quantum network – must account for special and general relativistic effects
We explore the propagation of relativistic wavepackets along an arbitrary null geodesic in a general curved spacetime geometry, and show how the curvature of the spacetime geometry distorts the wavepacket as it travels along the null geodesic
We start by considering a relativistic massless scalar field ψ ≔ ψ that propagates in a curved spacetime geometry xμ = (t, xi)
Summary
The current race in quantum communication – endeavouring to establish a global quantum network – must account for special and general relativistic effects. In Supplementary Note 2, we prove that in the Lorentz gauge, each linear polarisation of the photon in a curved spacetime geometry gets corrected as if it were a massless scalar field. It is reported that the Riemann tensor quantum mechanically alters the wavepacket propagating along a geodesic.
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