Abstract For ultra-long-distance free-space quantum communication such as satellite-to-ground quantum key distribution, decoherence is conventionally described by an exponential decay model. Such exponential environmental decoherence theory works well for short and medium propagation distances, yet its validity over thousands of kilometers of vacuum transmission remains open to discussion. This work proposes a phenomenological model of intrinsic vacuum coherence leakage for freely propagating entangled photons. Different from traditional exponential decoherence, the model predicts sub-exponential decay of entanglement fidelity with propagation distance. Numerical comparison indicates that the two models yield nearly identical predictions at short distances, while obvious deviations gradually emerge for ultra-long transmission. We further derive the modified secure key rate under the sub-exponential dissipation model. The theoretical prediction is testable using existing space-ground quantum experimental platforms. This preprint provides a new candidate framework to describe quantum channel behavior for deep-space and ultra-long-range quantum communication. This manuscript is released as a preprint for open discussion and academic archiving. No references are attached in the initial version; supplementary citations will be added for subsequent formal journal submission.
Abstract For ultra-long-distance free-space quantum communication such as satellite-to-ground quantum key distribution, decoherence is conventionally described by an exponential decay model. Such exponential environmental decoherence theory works well for short and medium propagation distances, yet its validity over thousands of kilometers of vacuum transmission remains open to discussion. This work proposes a phenomenological model of intrinsic vacuum coherence leakage for freely propagating entangled photons. Different from traditional exponential decoherence, the model predicts sub-exponential decay of entanglement fidelity with propagation distance. Numerical comparison indicates that the two models yield nearly identical predictions at short distances, while obvious deviations gradually emerge for ultra-long transmission. We further derive the modified secure key rate under the sub-exponential dissipation model. The theoretical prediction is testable using existing space-ground quantum experimental platforms. This preprint provides a new candidate framework to describe quantum channel behavior for deep-space and ultra-long-range quantum communication. This manuscript is released as a preprint for open discussion and academic archiving. No references are attached in the initial version; supplementary citations will be added for subsequent formal journal submission.
Long-distance, entanglement distribution over thousands of kilometers is necessary to build a global-scale quantum network. Directly transferring entangled, telecom photons through fiber is relatively straight forward in local networks where the separation between nodes is below 100 km, corresponding to a 1% transmission. However, the exponentially greater loss at larger distances (e.g. only 10−6 transmission at 300 km) leads to unacceptably low transmission rates, which drop below the noise rates of typical photon detectors. Alternatively, the Earth’s rarefied atmosphere at high altitudes reduces the absorption and scattering of infrared photons. Therefore, free-space links between satellite and ground stations have been shown to enable entangled photon transmission over 2000 km. While this demonstration showed the viability of satellite-enhanced entanglement distribution, the source used in this demonstration produced distinguishable photons, which cannot be used for many fundamental protocols like teleportation. We are building a testbed to demonstrate the feasibility of distributing entangled, indistinguishable photons over a space-to-ground link using entanglement swapping.
Abstract: Terrestrial fiber-optic quantum networks are subject to exponential photon attenuation (≈ 0.2 dB/km at 1550 nm), constraining unrepeatered ground quantum key distribution (QKD) and entanglement distribution to distances below a few hundred kilometers. While quantum repeaters remain technologically nascent, intercontinental sovereign security mandates unhackable, physical-layer cryptographic connectivity across transoceanic baselines. Satellite-based quantum communications operating in Low Earth Orbit (LEO, altitude h ≈ 500–800 km) provide a transformative solution by exploiting near-vacuum propagation for the vast majority of the optical path, bypassing terrestrial exponential loss. However, high-velocity LEO satellite platforms (v ≈ 7.6 km/s) introduce severe relativistic and atmospheric distortions that rapidly destroy quantum coherence: (1) kinematic Doppler shifts (Δν/ν ≈ ± 2.5 × 10^-5) and general relativistic gravitational redshifts alter photon wavepackets and relative phase trajectories; (2) dynamic spacetime curvature induces Wigner phase rotations on polarization-entangled states; and (3) atmospheric turbulence creates beam wandering, wavefront aberration, and photon arrival time jitter across the troposphere (0–15 km). This monograph establishes the theoretical framework, mathematical formulation, and solid-state engineering architecture for the PHOENIX_ORBIT space-to-ground quantum communications network. We derive: (1) an exact relativistic transformation matrix incorporating Kerr-Schwarzschild spacetime metric perturbations and orbital kinematics, coupled to an ultra-fast electro-optic dynamic phase compensator operating with sub-picosecond latency; (2) an adaptive optics (AO) closed-loop architecture combining high-bandwidth tip-tilt mirrors and deformable piezo-actuators calibrated to the local Fried parameter r_0 and Greenwood frequency f_G; (3) an entanglement routing protocol linking space-borne spontaneous parametric down-conversion (SPDC) sources to ground-based PHOENIX_ROUTER quantum data centers; and (4) an asymptotic security proof verifying Clauser-Horne-Shimony-Holt (CHSH) Bell inequality violation (S ≥ 2√2 − ε) under non-inertial reference frame drift. Our architecture achieves a continuous secret key rate exceeding 1.2 Mbps per satellite pass with a quantum bit error rate QBER < 1.4%, providing an unassailable physical-layer foundation for global sovereign data sovereignty.
Quantum decoherence is traditionally modeled through empirical decay laws in which observable coherence decreases with time. While these models successfully describe the dynamics of open quantum systems, they do not by themselves explain the physical destination of the apparently lost coherence. Motivated by the Structured Quantum Noise (SQN) framework, which models noise as a structured quantum subsystem rather than a scalar attenuation parameter, this paper proposes an information-theoretic interpretation of decoherence as coherence redistribution into environmental degrees of freedom. We introduce the concept of a Noise Black Hole, a hierarchical environmental structure through which coherence and entanglement diffuse into progressively less accessible sectors while remaining globally conserved. A minimal coherence-retention model shows that the familiar exponential decoherence law emerges naturally from repeated information redistribution rather than being imposed phenomenologically. The framework further predicts that deviations from ideal exponential decay arise from differences in environmental structure, memory, coupling, and backflow pathways, suggesting that measured decoherence curves may provide indirect probes of otherwise inaccessible environmental Hilbert-space dynamics. Rather than modifying conventional open-system theory, the proposed framework provides a possible information-theoretic explanation for the observed form of decoherence while generating experimentally testable predictions.
This work establishes a quantitative entanglement model built upon the vacuum quantum medium hypothesis. Instead of postulating instantaneous wave‑function collapse and intrinsic randomness, entanglement is interpreted as long‑range synchronized coupling among particles mediated by vacuum medium units. Based on geometric shell‑layer packing constraints of medium units, this model derives a finite critical distance for stable entanglement coupling. Entanglement completeness decays in piecewise fashion with particle separation, and environmental disturbances including geomagnetic field, thermal noise and ionospheric effects are introduced as multiplicative correction coefficients. Corresponding deterministic spin‑synchronization geometric formulas replace the stochastic probability framework of Bell‑inequality statistics. Extensions to multi‑particle GHZ‑type network entanglement are also provided. Calculated results show reasonable order‑of‑magnitude consistency with existing experimental observations including the Micius satellite‑ground entanglement test. A falsifiable prediction is put forward: under near‑Earth ionospheric‑geomagnetic conditions, entanglement synchronization signals will exhibit a steep cliff‑style drop within the 1400–1490 km distance interval. Light‑weight engineering formulas are supplied for rapid practical estimation. This model offers an alternative deterministic geometric description for quantum entanglement phenomena.
This paper introduces the Entanglement Propagation Damping (EPD) model, a theoretical framework designed to quantify and explain the observed loss of entanglement during its transmission through quantum networks. The core premise of EPD is that entanglement, while initially robust, experiences a gradual attenuation – a damping – due to various environmental interactions. This damping is characterized by a coefficient, γE, which represents the rate at which entanglement degrades. The model builds upon existing research concerning decoherence and dissipation, proposing a more refined approach that explicitly incorporates the propagation of entanglement and its susceptibility to damping factors. The EPD model provides a potential framework for understanding and mitigating entanglement loss, with implications for the development of long-distance quantum networks and potentially deserving of consideration for Nobel Prize recognition. The model offers a novel perspective on the fundamental limitations of entanglement distribution and presents a quantifiable metric for assessing the effectiveness of various entanglement protection strategies.
The realization of the quantum internet as an interconnected network of quantum hardware requires the distribution of entanglement over long distances. Due to the exponential photon loss in optical fibers, the necessary communication rates for end-user applications cannot be achieved if direct links over several hundred kilometers are required. Two possible solutions to increase the link distance are the implementation of quantum repeaters and the use of free-space optical satellite links. A natural extension would be to combine both approaches, by using satellites as quantum repeater nodes and take advantage of the low losses in free-space. However, due to the higher technological requirements for space-based technologies and the already low communications losses in free-space, it is not yet clear whether satellite- based quantum repeaters can lead to an additional improvement in the communication rate. Here we show for which operating scenarios a satellite-based quantum repeater outperforms a single satellite for entanglement distribution. To this end, we developed a satellite simulation software that includes a model of the optical link model and of entanglement swapping in order to analyze entanglement distribution rates of the satellite-based quantum repeater and single satellite. The simulation captures important effects such as the single-mode fiber coupling efficiency, adaptive optics corrections, decoherence and decay of information in the quantum memory as well as its retrieval efficiency. Based on these effects, we show advantages and challenges of satellite constellations for quantum communications in low, medium and geosynchronous orbits.