A physically consistent description models turbulence-induced loss for non-classical signalling models each hop as a pure-loss bosonic channel whose random transmissivity follows a truncated Gamma-Gamma law, conditioned on the physically admissible range of transmittance. Under this channel, coherent states remain pure, whereas squeezed states are mapped to mixed Gaussian states. For Helstrom-optimal detection, the average error of the coherent hop is derived by exact Laplace-series form analysis.

For the decode-and-forward (DF) hop with displaced squeezed states (DSS), output states are derived, along with a closed-form Gaussian fidelity and rigorous two-sided bounds on the Helstrom error; it is also proven that an optimal photon partition exists considering loss effects. Furthermore, optimised squeezing preserves both the turbulence-induced diversity order and the leading asymptotic constant of coherent relaying, indicating its benefit arises from finite-photon budget considerations, and an interior throughput-optimal harvesting fraction exists. A covariance-preserving benchmark yields an analytical upper bound on achievable throughput which provides absolute gap vanishes as the relay photon budget grows.

Numerical results based on exact mixed-state Helstrom error quantify the benefits of squeezing and identify the regime where it proves useful. The objectives are to develop a unified framework for relay-assisted quantum free-space optical (FSO) communication with optical energy harvesting (EH) and DSS signalling, enabling fundamental characterisation of reliability and achievable throughput in energy-constrained systems under turbulence impairments using Helstrom-optimal detection.

The analysis builds upon tools such as quantum Chernoff bound, Fuchs, van de Graaf inequalities, and time-switching DF relaying principles. Specific contributions include: developing a physically consistent framework for EH quantum relays with TS-DF architecture; providing an exact characterisation of DSS hop behaviour including output state derivation, fidelity calculation, and Helstrom error bounding; proving the existence of a loss-aware optimal photon partition differing from lossless rules; demonstrating that optimised squeezing preserves coherence benefits under turbulence while offering finite gains; characterising the throughput-optimal harvesting design alongside a rigorous upper bound on achievable throughput which converges as the photon budget increases.

Squeezed Signalling Enables Scalable Gains in Turbulent Free Space Optics

An exact series representation for covariance preservation was achieved within a benchmark system, a level of precision previously unattainable, enabling detailed modelling of complex free-space optical (FSO) communications systems. Optimised squeezing improves upon existing methods by simultaneously preserving both the diversity of order induced by turbulence *and* the leading asymptotic constant associated with coherent relaying; prior approaches sacrificed one to gain the other, limiting performance scaling.

This breakthrough allows gains dependent on photon budget while maintaining similar scalability to traditional FSO techniques, offering practical benefits through optimised energy use and demonstrating that finite resources can enhance communication reliability over turbulent air using displaced squeezed signalling alongside time-switching optical energy harvesting at decode-and-forward relays.

The system models each transmission ‘hop’ as a pure-loss bosonic channel, accurately reflecting how atmospheric turbulence affects non-classical signals like squeezed states which become mixed Gaussian states during transit. An analytical upper bound on achievable throughput is provided by a covariance-preserving benchmark utilising an exact series representation; its gap vanishes as the relay photon budget increases, meaning performance improves predictably with more photonic resources.

Numerical results quantifying Helstrom error confirm squeezing’s benefits and identify when it boosts signal reliability most effectively. Increasing the number of photons allocated to the system generally enhances performance, but diminishing returns occur beyond a certain point due to practical limitations.

Photonic resource allocation balances quantum gain against realistic relay power limitations

This work offers a pathway towards more reliable long-distance quantum communication through optimised encoding of information onto light using ‘displaced squeezed signalling’, minimising disruption from atmospheric turbulence, but highlights an ongoing tension within free-space optical links: balancing theoretical gains with practical energy constraints at the relay station itself. Careful photonic resource allocation between signal displacement and squeezing can preserve performance scaling while benefiting from limited power budgets; this approach assumes ideal conditions for time-switching optical energy harvesting. However, acknowledging that ideal conditions are rarely met in reality is important, as atmospheric variations will inevitably impact the efficiency of powering these relays.

By combining displaced squeezed signalling with time-switching optical energy harvesting at relay stations, a framework for reliable quantum communication over free-space optical links has been established. In particular, their analysis demonstrates careful photon allocation preserves existing performance limits *and* benefits from limited resources, a significant improvement because previous methods required trade offs in scalability or reliability. This optimisation process considers factors like signal strength and environmental noise to maximise data transmission rates under realistic operating constraints.

This research demonstrated that using ‘displaced squeezed signaling’ alongside an optically powered relay station can improve the reliability of transmitting information via light through turbulence. The study found that carefully allocating photonic resources, balancing signal displacement with squeezing, maintains predictable performance scaling even when power is limited at the relay.

Analysis showed optimized squeezing preserved established communication limits while benefiting from finite photon budgets; furthermore, increasing the number of photons generally improved system performance up to a point. These findings establish a framework for achieving reliable quantum communication over free-space optical links by addressing both signal quality and energy efficiency.

👉 More information
🗞 Time-Switching Energy-Harvesting Quantum Relay-Assisted FSO Communication with Displaced Squeezed Signaling
✍️ Nizar Khalfet and Ioannis Krikidis (Department of); Francisco A. Monteiro (Instituto de Telecommunicac¸˜)
🧠 ArXiv: https://arxiv.org/abs/2610.39091

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