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.
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.
There has been considerable interest over the past years in investigating the role of gravity in quantum phenomenon such as entanglement and decoherence. In particular, gravitational time dilation is believed to decohere superpositions of center of mass of composite quantum systems. Since true effects of gravity are encoded in the curvature of spacetime, the universality of such decoherence must be characterized through components of Riemann tensor Rabcd, with a clear separation from non-inertial kinematic effects. We obtain the reduced density matrix of a composite system in a generic curved spacetime and express the decoherence time scale explicitly in terms of curvature. The decoherence in an inertial frame is caused by tidal acceleration. We also analyze the effects of self-gravity and show that the coupling of gravitational interaction with external curvature can not be captured by the replacement m→m+Hint/c2.
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.
We study how quantum systems that propagate in the spacetime of a rotating planet are affected by the curved background. Spacetime curvature affects wavepackets of photons propagating from Earth to a satellite, and the changes in the wavepacket encode the parameters of the spacetime. This allows us to evaluate quantitatively how quantum communications are affected by the curved spacetime background of the Earth and to achieve precise measurements of Earth's Schwarzschild radius and equatorial angular velocity. We then provide a comparison with the state of the art in parameter estimation obtained through classical means. Satellite to satellite communications and future directions are also discussed.
In this thesis we study relativistic effects on quantum systems. Quantum physics in curved spacetime is reviewed in a first place, with a focus on continuous variables formalism, quantum metrology techniques, and the relativistic treatment of polarised photons. Then, three topics of interest are studied. The first one is the phononic gravitational wave detector, where resonant mode-mixing and particle creation are triggered in a Bose-Einstein condensate by the passing of a gravitational wave, which can then be measured thanks to quantum metrology techniques. The theory for the phonons’ transformation is developed in details in different resonance scenarios and some sources of noise are considered, like shaking of the cavity where the condensate is trapped and thermal noise. The second topic adressed is quantum communication and metrology in space. In this part, we describe quantum experiments involving communications between Earth and satellites using frequency modes of photons. The propagated and measured photons encode parameters of the spacetime background that can be measured using quantum metrology. Several satellite schemes are discussed, such as satellite to satellite radial communications in Kerr spacetime or Earth to satellite communications in Schwarzschild spacetime. The last topic of this thesis is the evolution of helicity states of photons in a relativistic picture. Two experiments are considered: one where the photons propagate between Earth and satellites through the curved spacetime background surrounding the Earth. The other experiment looks at quantum states of polarised photons as seen by centrifuged observers. For each of these parts, we provide the theory for novel experimental proposals, within the frameworks of either (or both) quantum communications and quantum metrology, that, we believe, would lead to a better understanding in the overlap of quantum mechanics and the relativity theories.
Classical clocks measure proper time along their worldline, and Riemannian geometry provides tools for predicting the time shown by clocks in both flat and curved spacetimes. Common approaches to time in quantum systems, based for instance on wave functions or density matrices, tend to obscure this geometric property at the quantum level. Here, a new framework is demonstrated for perturbing the classical path-length functional to include quantum degrees of freedom within a modified Riemannian geometry. In this framework, a quantum clock travels on geodesics of a family of spacetimes deformed by parameters specifying the clock's quantum state. Detailed derivations provide potentially testable corrections to gravitational time-dilation in Schwarzschild spacetime that scale with the ratio of the clock's Compton wavelength to its wave packet's spatial extent.
This paper investigates the theoretical feasibility of quantum information transmission leveraging artificially induced spacetime distortions. The core claim proposes that controlled spacetime curvature, mimicking the effects predicted by General Relativity, can facilitate quantum information transfer between entangled particles over distances exceeding the limitations imposed by the speed of light. The proposed mechanism utilizes a specifically designed apparatus capable of generating a localized, simulated spacetime distortion. This distortion, in turn, alters the effective distance between entangled particles, allowing for instantaneous information correlation despite the spatial separation. Mathematical modeling and key equations are presented to illustrate the theoretical framework, including the relationship between spacetime curvature, quantum entanglement, and information transfer rates. The potential implications of this approach for future quantum communication technologies are discussed, acknowledging the significant technological challenges involved in realizing such a system. The central focus remains on the theoretical exploration of this novel paradigm, providing a foundational understanding for potential future research.