Free-space optical (FSO) links supporting spatial multiplexing provide a natural physical realization of Quantum MIMO channels. We develop a first-principles model for Quantum MIMO channels derived directly from wave-optical propagation through three-dimensional atmospheric turbulence. The framework explicitly accounts for intermodal crosstalk, finite detection apertures, and the system-bath separation induced by spatial-mode projection. We distinguish between distinguishable and indistinguishable photon regimes, showing that indistinguishability leads to intrinsically many-body interference effects described by matrix permanents. To obtain a completely positive and trace-preserving logical description, we introduce an erasure-extended encoding in which turbulence-induced leakage and photon loss are mapped to flagged erasure states. The resulting Quantum MIMO channel naturally reduces to a correlated n-qubit erasure channel, with correlations arising from the shared turbulent medium. Limiting regimes in which correlated Pauli channels emerge as effective approximations are also identified.
Free-space optical (FSO) links supporting spatial multiplexing provide a natural physical realization of Quantum MIMO channels. We develop a first-principles model for Quantum MIMO channels derived directly from wave-optical propagation through three-dimensional atmospheric turbulence. The framework explicitly accounts for intermodal crosstalk, finite detection apertures, and the system-bath separation induced by spatial-mode projection. We distinguish between distinguishable and indistinguishable photon regimes, showing that indistinguishability leads to intrinsically many-body interference effects described by matrix permanents. To obtain a completely positive and trace-preserving logical description, we introduce an erasure-extended encoding in which turbulence-induced leakage and photon loss are mapped to flagged erasure states. The resulting Quantum MIMO channel naturally reduces to a correlated n-qubit erasure channel, with correlations arising from the shared turbulent medium. Limiting regimes in which correlated Pauli channels emerge as effective approximations are also identified.
Free-space optical (FSO) links carry quantum states without fiber, but diffraction, pointing error, and atmospheric turbulence couple spatial modes and reduce end-to-end fidelity. Classical multiple-input multiple-output (MIMO) uses spatial channels for multiplexing or diversity. For unknown quantum states, however, the no-cloning theorem prevents classical replication. We therefore formulate an FSO quantum multiple-input multiple-output (QuMIMO) link for an unknown polarization qubit as a single completely positive and trace-preserving (CPTP) map. It combines passive field transfer, bosonic pure loss lifted to Fock space, a receiver map to erasure-augmented polarization qubits, and effective per-port polarization noise. The plane-wave Rytov variance parameterizes turbulence, while an internal-state Gram matrix captures partial photon distinguishability and its effects on path coherence and multiphoton interference. Using Haar-averaged state fidelity, we compare direct transmission, fixed quantum error correction (QEC), approximate quantum cloning, coherent path superposition, and channel-adapted encoder and recovery maps, while distinguishing channel state information (CSI) from endpoint availability. With Full CSI on the two-rail channel, asymmetric cloning and coherent path superposition exceed the fixed single-input single-output (SISO) baseline in average fidelity. Adding rails and their admitted photon-number sectors enlarges the attained general-CPTP gain over the fixed SISO baseline, with the widest margin at moderate turbulence. Fixed stabilizer encoders perform poorly as turbulence makes rail survival unequal and produces errors unlike erasures at known code positions. Thus, QuMIMO realizes channel-adapted spatial diversity without requiring multiple copies of the logical qubit.
We develop an exact error probability framework for quantum free space optics (FSO) communication over atmospheric channels with turbulence and pointing errors under a physically admissible bounded transmissivity model. The proposed framework is grounded in the fundamental physical observation that, in a quantum optical channel, the random channel quantity is the transmissivity itself, namely, the fraction of transmitted photons collected at the receiver, and must therefore take values only in the physically admissible interval [0,1]. This constraint is generally violated when classical turbulence models are interpreted directly as transmissivity models in quantum settings. Accordingly, we model the turbulence-induced transmissivity as a Beta distributed random variable over (0,1), which has recently been shown to provide accurate fitting under different turbulence conditions while preserving physical admissibility. We then integrate deterministic atmospheric loss and pointing errors into a unified equivalent transmissivity model and derive exact expressions for its probability density function and moment generating function. Building upon this statistical characterization, we derive novel exact average error probability expressions for binary modulation under both quantum and classical receivers. Finally, we verify the analysis using Monte Carlo simulations, quantify the impact of turbulence and pointing errors, and demonstrate the performance advantage of quantum optimal detection in photon-limited quantum FSO channels.
We consider the schemes that would lead to the increase in the channel capacity of free space optical links (FSO) and propose a novel orthogonal angular momentum (OAM)- and WDM-based MIMO architecture for highspeed QKD in turbulent FSO channels. We evaluated the dependence of OAM-based interference, which notably affects QBER, from the number of OAM states and the turbulence strength. The scheme is numerically verified to support ≥1Mb/s QKD rates in km-scale turbulent links using 5 OAM states and 80 wavelengths.
Understanding the influence of atmospheric turbulence on the propagation of entangled biphoton states is essential for free-space quantum communication protocols. Using the extended Huygens-Fresnel principle and the Kolmogorov turbulence model, we derive an analytical expression for the combined density operator of the signal and idler fields generated via SPDC, following propagation through separate turbulent channels. By expressing this density operator in the continuous position basis, we show how the spatial correlations between signal and idler persist through turbulence despite the loss of state purity, as they transition from being quantum to classical in nature. We further identify a finite range of propagation distances over which the angle-OAM entanglement is maximized, which provides valuable insights for designing free-space quantum communication links operating over several kilometers through the turbulent atmosphere.
Abstract Spatial multiplexing can increase the rate of entanglement distribution over free-space optical (FSO) channels, but atmospheric turbulence introduces modal crosstalk and unequal loss among spatial modes. We propose adaptive spatial multiplexing (ASM), which uses channel state information (CSI) for each coherence block and singular value decomposition (SVD)-based transmit–receive processing to adapt the spatial basis and the number of Bell pairs distributed in parallel. For a passive, polarization-independent channel with at most one photon in each selected singular input mode, vacuum in every unused input mode, and a portwise receiver that preserves polarization qubits in singly occupied output modes and maps all other occupations to erasures, matched SVD processing reduces the collected multiphoton channel to parallel qubit erasure channels with transmissivities given by the squared singular values of the transmission matrix. The resulting one-way hashing rates are additive and nonnegative. Therefore, when the minimum per-stream rate is the only constraint on selection, the aggregate achievable rate is maximized exactly by selecting every parallel channel that meets it. We study ASM over a simulated four-mode turbulent FSO channel ensemble with ideal, polarization-preserving mode processors. At the nominal minimum-rate requirement, ASM outperforms receiver-only combining in aggregate rate, per-stream rate, and priority-stream non-outage probability. The results show that ASM turns spatial multiplexing into a resource-aware strategy for entanglement distribution, balancing overall throughput with stream reliability and photon efficiency. Its aggregate-rate advantage over receiver-only processing persists under the CSI-aging conditions considered.
We investigate the performance of relativistic quantum key distribution (RQKD) over turbulent free-space optical channels for both single-photon and coherent-state implementations. A theoretical model is developed to describe the effect of atmospheric turbulence on interferometric visibility and secret-key generation by incorporating turbulence-induced phase fluctuations into the key-rate analysis. Numerical simulations are performed under realistic channel conditions to evaluate the achievable communication distance and secret-key rate. The results show that atmospheric turbulence degrades the protocol performance by reducing interference visibility, with the severity of the degradation determined by the ratio between the interferometer-arm separation r (or temporal separation of signal and reference states ΔT) and Fried's parameter. The single-photon protocol remains operational over all investigated turbulence regimes, whereas the coherent-state implementation exhibits a critical dependence on the interferometer geometry (especially on ΔT), leading to a threshold beyond which secure key generation is no longer possible. These findings quantify the impact of atmospheric turbulence on relativistic quantum key distribution and provide practical guidelines for the design and optimization of free-space RQKD systems.