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.
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.
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.
Entanglement is key quantum information processing feature enabling quantum communication, networking, and sensing [1]. Unfortunately, long-distance quantum communication is affected by the photon loss, given that quantum signals cannot be amplified. As an alternative, free-space optical (FSO) links can be used instead for entanglement distribution. However, the FSO links are severely affected by atmospheric turbulence effects, in addition to scattering effects. In this paper, we demonstrate that adaptive optics [2] is a useful tool to improve fidelity of entanglement when entangled states are distributed over turbulent FSO links. We present results from our FSO communication experiment where we generated entangled photons pairs, launched them into free-space, and later collected them for coincidence count measurement. We demonstrate that adaptive optics can be used to make improvements in coincidence counts.
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.
Quantum key distribution (QKD) provides information-theoretic security and satellite-based quantum key distribution (SatQKD) has demonstrated the potential to extend this communication security to intercontinental scales. However, atmospheric turbulence induces significant distortion in the spatial distribution of received optical beams, while background noise remains approximately uniform across the detector plane. As a result, single-element qubit (quantum bit) detection can be frequently dominated by noise due to the random spatial pattern of the imaged wavefront, thereby degrading the system performance. To address this limitation, we propose to exploit the spatial degrees of freedom of single-photon detector arrays to reject the excessive noise while adapting to channel variations induced by turbulence. We develop a threshold-based selection method that only activates detector elements that have higher probability of registering qubits. We evaluate the performance of the proposed noise-rejection QKD schemes using Monte Carlo simulations considering the impact of diffraction and atmospheric turbulence on the transmitted optical beam in the presence of background and dark noise. The results show that, compared to conventional schemes, the proposed noise-rejection strategy effectively reduces the quantum bit error rate (QBER) and improves the secret key rate (SKR) performance, while the performance gains depend on the turbulence condition. These findings demonstrate the potential of adaptive array receiver design to enhance the robustness of the SatQKD system under realistic atmospheric conditions.
Transmitting a beam through the atmosphere over long distances can be a challenging problem. Factors from the channel, such as atmospheric turbulence causing beam wander and distortions to the wavefront, or the optical design can change the loss induced in the channel. This work simulates a quantum key distribution system implementing the BB84 protocol with entangled photons operating over a 30 km maritime channel using one, four, and nine spatial modes. For the cases of multiple spatial modes, atmospheric turbulence increases the channel cross talk, resulting in an increase in the noise for each channel. To compensate for distortions in the wavefront, adaptive optics at the transmitter or receiver are used to pre- or post-correct the wavefront.
Optical communication with high photon-efficiency (many bits/photon) and high spectral efficiency (SE) (many bits/s-Hz) cannot be achieved unless multiple spatial modes are employed. For vacuum propagation, it is known that achieving 10 bits/photon and 5 bits/s-Hz requires 189 low-loss spatial modes at the ultimate Holevo limit and 4500 such modes at the Shannon limit for on-off keying with direct detection. For terrestrial propagation paths, however, atmospheric turbulence corrupts multiple spatial-mode operation. This paper derives power-transmissivity bounds and average intermodal crosstalks for the turbulent channel that depend solely on the mutual coherence function of the atmospheric Green's function. These statistics are then evaluated for ~ 200 spatial-mode systems whose transmitters use either focused-beam, Hermite-Gaussian (HG), or Laguerre-Gaussian (LG) modes and whose receivers either do or do not employ adaptive optics. It is shown that: (1) adaptive optics are not necessary for achieving both high photon information efficiency (PIE) and high SE; (2) systems employing HG or LG modes achieve the same capacities through turbulence; and (3) the orbital angular momentum carried by LG modes does not provide turbulence immunity. In the companion paper [N. Chandrasekaran, J. H. Shapiro, and L. Wang, “Photon Information Efficient Communication Through Atmospheric Turbulence-Part II: Bounds on Ergodic Classical and Private Capacities,” J. Lightw. Technol., vol. 32, no. 6, pp. 1088-1097, Mar. 2014], the transmissivity bounds are used to quantify the turbulence-induced loss in PIE versus SE performance for these mode sets.