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arXiv:2106.13426 · Physical Review A

Polarization rotation and near-Earth quantum communications

Pravin Kumar Dahal, Daniel R. Terno

Published Oct 28, 2021• 6 citations
arXivHTMLPDF

Abstract

We revisit polarization rotation due to gravity, known as the gravitational Faraday effect, with a view on its role in quantum communications with Earth-orbiting satellites. In a static spherically symmetric gravitational field Faraday rotation is purely a reference frame (gauge) effect. This is so also in the leading post-Newtonian expansion of the Earth's gravitational field. However, establishing the local reference frame with respect to distant stars leads to the nonzero Faraday phase. In communications between a ground station and an Earth-orbiting spacecraft this phase is of the order of ${10}^{\ensuremath{-}10}$. Under the same conditions the Wigner phase of special relativity is typically of the order ${10}^{\ensuremath{-}4}\ensuremath{-}{10}^{\ensuremath{-}5}$. These phases lead to the physical lower bound on communication errors. However, both types of errors can be simultaneously mitigated. Moreover, they are countered by a fully reference frame independent scheme that also handles arbitrary misalignments between the reference frames of sender and receiver.

DOI
10.1103/physreva.104.042610

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We revisit polarization rotation due to gravity, known as the gravitational Faraday effect, with a view on its role in quantum communications with Earth-orbiting satellites. In a static spherically symmetric gravitational field Faraday rotation is purely a reference frame (gauge) effect. This is so also in the leading post-Newtonian expansion of the Earth's gravitational field. However, establishing the local reference frame with respect to distant stars leads to the nonzero Faraday phase. In communications between a ground station and an Earth-orbiting spacecraft this phase is of the order of 10\ensuremath−10{10}^{\ensuremath{-}10}10\ensuremath−10. Under the same conditions the Wigner phase of special relativity is typically of the order 10\ensuremath−4\ensuremath−10\ensuremath−5{10}^{\ensuremath{-}4}\ensuremath{-}{10}^{\ensuremath{-}5}10\ensuremath−4\ensuremath−10\ensuremath−5. These phases lead to the physical lower bound on communication errors. However, both types of errors can be simultaneously mitigated. Moreover, they are countered by a fully reference frame independent scheme that also handles arbitrary misalignments between the reference frames of sender and receiver.
Abstract Satellite quantum and classical optical communication technologies have had rapid growth in the last decade. The polarization of the light is usually used to encode information or increase the data transfer speed in such systems. However, relative motion during the communication session causes the satellite’s and ground station’s polarization reference frames to spin mutually. We offer an analytical model for calculating the relative rotation of the polarization reference frame between the low Earth orbit satellite and the ground station. Based on the model, we simulate four typical satellite passage and analyze the polarization deviation angle between the satellite and the altazimuth ground telescope.
Abstract We describe the quantum mechanical rotation of a photon state, the Wigner rotation—a quantum effect that couples a transformation of a reference frame to a particle’s spin, to investigate geometric phases induced by Earth’s gravitational field for observers in various orbits. We find a potentially measurable quantum phase of the Wigner rotation angle in addition to the rotation of standard fame, the latter of which is computed and agrees well with the geodetic rotation. When an observer is in either a circular or a spiraling orbit containing non-zero angular momentum, the additional quantum phase contributes 10−6 degree to 10−4 degree respectively, depending on the altitude of the Earth orbit. In the former case, the additional quantum phase is dominant over the near-zero classical geodetic rotation. Our results show that the Wigner rotation represents a non-trivial semi-classical effect of quantum field theory on a background classical gravitational field.
Real global-scale quantum communications and quantum key distribution systems cannot be implemented by the current fiber and free-space links. These links have high attenuation, low polarization-preserving capability or extreme sensitivity to the environment. A potential solution to the problem is the space-earth quantum channels. These channels have no absorption since the signal states are propagated in empty space, however a small fraction of these channels is in the atmosphere, which causes slight depolarizing effect. Furthermore, the relative motion of the ground station and the satellite causes a rotation in the polarization of the quantum states. In the current approaches to compensate for these types of polarization errors, high computational costs and extra physical apparatuses are required. Here we introduce a novel approach which breaks with the traditional views of currently developed quantum-error correction schemes. The proposed solution can be applied to fix the polarization errors which are critical in space-earth quantum communication systems. The channel coding scheme provides capacity-achieving communication over slightly depolarizing space-earth channels.
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Abstract: Interplanetary exploration, crewed lunar and Martian settlements, and deep-space astronomical observatories demand unforgeable, high-bandwidth communication fabrics immune to spoofing, eavesdropping, and catastrophic data corruption. While near-Earth quantum key distribution (QKD) is viable across low Earth orbit (LEO, h ≤ 1,000 km), extending quantum entanglement to interplanetary baselines (R ∈ [0.1, 40] AU) confronts three extreme physical barriers: (1) catastrophic geometric photon dilution governed by the inverse-square law (η_geo ∝ R^-2), dropping received single-photon fluxes below 10^-15 over astronomical baselines; (2) massive general relativistic spacetime delays, Shapiro gravitational time dilation, and solar gravitational redshift that destroy temporal coincidence windows; and (3) solar wind plasma turbulence, interplanetary coronal mass ejections, and Faraday rotation that induce severe spatial and polarization decoherence. This monograph establishes the theoretical framework, mathematical formulation, and solid-state engineering architecture for PHOENIX_DEEP, an interplanetary quantum communications network designed for deep-space sovereign exploration: (1) We model the optical amplification of the Solar Gravitational Lens (SGL) at heliocentric distances b ≥ 547.5 AU, deriving a wave-optical brightness gain µ_SGL ≈ 10^5–10^6 that converts diverging single-photon beams into coherent pencil modes; (2) We derive an exact relativistic metric incorporating post-Newtonian (PPN) solar gravitational potential and Shapiro time delays, establishing a predictive feedforward temporal coincidence gate operating across multi-hour propagation regimes; (3) We design solid-state quantum memory relay nodes deployed at Sun-Earth and Earth-Moon Lagrange points (L2, L4, L5) utilizing europium-doped yttrium silicate (Eu^3+:Y2SiO5) crystals achieving optical coherence times T_2 > 1 hour under zero-first-order-Zeeman (ZEFOZ) fields; and (4) We formulate an asynchronous device-independent quantum key distribution (DI-QKD) protocol verifying Clauser-Horne-Shimony-Holt (CHSH) Bell inequality violations (S ≥ 2.724) across astronomical distances. Our architecture achieves a continuous secret key rate exceeding 11.6 kbps at Earth-Mars quadrature (1.5 AU) and 185.6 kbps across 16-channel DWDM links, establishing an unassailable physical-layer communication infrastructure for interplanetary human civilization.
The Kerr metric of a spherically symmetric gravitational field is analyzed through the coordinate transformation from a rotating frame to a fixed frame, and consequently that the inertial force field (with the exception of the centrifugal force field) in the rotating system is one part of its gravitomagnetic field is verified. We investigate the spin-rotation coupling and, by making use of Lewis-Riesenfeld invariant theory, we obtain exact solutions of the Schródinger equation of a spinning particle in a time-dependent rotating reference frame. A potential application of these exact solutions to the investigation of Earth's rotating frequency fluctuations by means of neutron-gravity interferometry experiment is briefly discussed in the present paper.