Towards Communication in a Curved Spacetime Geometry

Abstract

The current race in quantum communication, endeavouring to establish a global quantum network, must account for special and general relativistic effects. For example, Shapiro time-delay, gravitational lensing, and frame dragging -all due to how a mass distribution alters geodesics -are well-studied. 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 0.11 radian phaseshift for communication between Earth and the International Space Station on a monochromatic laser beam as well as quadrupole astigmatism, which causes 13.4% crosstalk among the modes, when structured modes traverse 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.

Spacetime effects on wavepackets of coherent light

“…In order to univocally identify the gravitational effects on the quantum coherence present in the state, we introduced a phase parameter that dictates the unavoidable relative phase contribution to the quantum coherence of each component in the superposition that defines the state. Our results (34) and (35) explicitly show that such phase parameter governs the deviation of the pure-state case with respect to the mixed state case. When the parameter vanishes, the pure state and mixed state scenarios give the same result.…”

“…The effects of the (weakly) curved spacetime surrounding the Earth on the frequency profile of photons propagating between two users placed at different heights in the gravitational potential have been considered recently in order to provide realistic modelling of quantum communication setups [30][31][32]. More detailed analysis of propagation in arbitrary curved backgrounds has also been recently considered by computing including the distortion effects of curvature on propagating pulses of light in the dimensions orthogonal to the path of propagation [35]. Here we will employ the original approach [30][31][32] and will assume that transversal deformations can be safely ignored.…”

“…We assume that we can model a photon as a wavepacket of the solutions u k (x µ ) to the field equations u k (x µ ) = 0, and that we can exclude all effects, such as dispersion and diffraction, suffered by the photon during propagation [30]. We then assume that the photon is fundamentally confined in the direction of propagation, and therefore we neglect to first approximation the effects of the dimensions orthogonal to the propagation (extra dimensions can be included if necessary [35]). Other effects of propagation in curved spacetimes can also be studied and included [36,45,46].…”

“…Modelling of realistic scenarios will additionally require the extension of our work to 3 + 1 dimensions, which has been preliminary investigated already [35]. This can be done and analytical results can be sought, however, it is known that solving the field equations in 3 + 1 curved spacetime ultimately requires numerical approaches.…”

“…More recently, complementary work has quantified the distortion of the wavepacket in the degrees of freedom perpendicular to the path of propagation [35]. Together, this body of research provides a better understanding of the effects incurred by photons that propagate in curved spacetimes.…”