How Many Qubits Can Be Teleported? Scalability of Fidelity-Constrained Quantum Applications

THIS IS AN A UTHOR-CREA TED POSTPRINT VERSION. Disclaimer: This work has been accepted for publication in the Joint Eur opean Conference on Networks and Communications & 6G Summit (EuCNC/6G Summit) , 2026. Copyright: © 2026 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in an y current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collectiv e works, for resale or redistribution to servers or lists, or reuse of an y copyrighted component of this work in other works. Ho w Man y Qubits Can Be T eleported? Scalability of Fidelity-Constrained Quantum Applications Oscar Adamuz-Hinojosa, Jonathan Prados-Garzon, Sara V aquero-Gil, Juan M. Lopez-Soler Department of Signal Theory , T elematics and Communications, Uni versity of Granada. Email: {oadamuz,jpg,juanma}@ugr .es; sarav aquerogil@correo.ugr .es Abstract —Quantum networks (QNs) enable the transfer of qubits between distant nodes using quantum teleportation, which repr oduces a qubit state at a remote location by consuming a shared Bell pair . After teleportation, qubits are stored in quantum memories, where decoherence progressi vely degrades their quantum states. This degradation is quantified by the fidelity , defined as the overlap between the stored quantum state and the ideal target state. Some quantum applications (QApps) requir e the teleportation of multiple qubits and can only operate if all teleported qubits simultaneously maintain a fidelity above a giv en thr eshold. In this paper , we study how many qubits can be teleported under such fidelity-constrained operation in a two-node QN. T o that end, we define a QApp- level reliability metric as the probability that all end-to-end Bell pairs satisfy the target fidelity upon completion of the multi-qubit teleportation stage. W e design a Monte Carlo–based simulator that captures stochastic Bell-pair generation, Quantum Repeater (QR)-assisted entanglement distrib ution, and fidelity degradation. Fiber -based and terr estrial free-space optical (FSO) quantum links and representativ e NV -center - and trapped-ion- based quantum memories are considered. Results show that memory coherence is the main scalability bottleneck under stringent fidelity targets, while parallel entanglement generation is essential for multi-qubit teleportation. Index T erms —fidelity , quantum applications, parallel entan- glement generation, quantum r epeaters, quantum teleportation. I . I N T RO D U C T I O N Unlike classical information, quantum information is en- coded in fragile quantum states that cannot be copied or regenerated without disturbance. Consequently , the physical transmission of qubits over long distances is severely limited by loss and noise, and classical amplification techniques cannot be used to preserve quantum information [1], [2]. T o overcome this limitation, Quantum Networks (QNs) rely on quantum teleportation to transfer a quantum state from a source node (Alice) to a destination node (Bob) without phys- ically transmitting the qubit itself [3]. T eleportation consumes pre-shared entanglement in the form of Bell pairs and classical communication to reconstruct the quantum state at Bob. Many Quantum Applications (QApps) require an execution- gated phase in which multiple qubits must be transferred from Alice to Bob before quantum processing can start. This transfer relies on the prior establishment of a set of end-to- end Bell pairs. These Bell pairs are generated probabilistically and become a vailable at different times at Bob . Bell-pair qubits generated earlier must be stored in quantum memories, where decoherence de grades their quantum states over time. Execu- tion is feasible only if, when the teleportation phase is trig- gered, all required qubits are simultaneously a vailable at Bob while satisfying a minimum fidelity threshold. Here, fidelity is defined as the o verlap between the quantum state obtained after storage and the ideal target state [4]. Representative examples of such e xecution-gated multi-qubit QApps include distributed quantum computing [5], [6], entanglement-assisted sensing and synchronization [7], [8], and QN calibration and benchmarking [9], [10]. Motivation. Direct quantum teleportation between two nodes is limited by photon losses, which sharply reduce both the achiev able distance and the probability of successfully establishing the Bell pairs required for teleportation [2]. Quan- tum Repeaters (QRs) mitigate this limitation by partitioning a long quantum link into two shorter segments and using entanglement sw apping to distrib ute Bell pairs over extended distances, thereby enabling teleportation beyond the range of direct transmission [11]. This has motiv ated extensiv e research on QR-assisted QNs, including queueing-based models of Bell-pair generation and storage [12], continuous-time Markov models for entanglement switching [13], [14], [15], [16], and architectural performance analyses [17], [18]. While these works provide valuable insight into link- and protocol-lev el behavior , they do not address QApp-le vel success conditions. In particular , they do not quantify r eliability , defined as the probability that all qubits required by a QApp are simulta- neously av ailable with fidelity above a target threshold after storage in quantum memories. This limitation also applies to commonly used QN simulators [19], such as QKDNet- Sim+, NetSquid, or QuISP , whose abstractions do not capture continuous-time fidelity degradation during passive storage and therefore cannot assess the joint feasibility of multi-qubit teleportation under fidelity constraints. Contributions. In this paper , the central question addressed is: gi ven a QR-assisted QN with stochastic Bell-pair generation and quantum-memory decoherence, how many qubits can be teleported such that all of them simultaneously satisfy a tar get fidelity constraint? T o answer it, we ev aluate the scalability of multi-qubit, fidelity-constrained teleportation in two-node QNs assisted by a single QR. The main contributions are: C1) QApp-Le vel Reliability Metric: W e formulate a QApp-lev el r eliability metric that quantifies the probability that all Bell pairs required for a multi-qubit teleportation phase are simultaneously a vailable with fidelity above a tar get threshold, jointly capturing stochastic entanglement genera- tion, parallelism, and memory decoherence. C2) Reliability-Oriented Simulation Framework: W e dev elop a dedicated simulator, based on Monte Carlo, that captures stochastic Bell-pair generation, parallel entangle- ment attempts, QR-assisted entanglement distribution, and continuous-time fidelity degradation in quantum memories, enabling the ev aluation of QApp-lev el reliability . C3) Feasibility Analysis Across T echnologies: W e char- acterize the feasible regions in which a giv en number of qubits can be teleported while satisfying target fidelity and reliability constraints, and assess how these regions depend on the underlying quantum-memory technology , i.e., Nitrogen- V acanc y (NV)-based centers or trapped ions, and the transmis- sion medium, i.e., optical fiber or terrestrial Free-Space Optical (FSO). Paper Outline. Section II re views the fundamentals of QN. Section III presents the system model. Section IV introduces the QApp-lev el reliability formulation. Section V describes the simulation setup. Section VI discusses the results, and Section VII concludes the paper . I I . F U N DA M E N TA L S A. Qubits and Quantum Entanglement A qubit is the fundamental unit of quantum information and can be expressed as a coherent superposition | ψ ⟩ = a | 0 ⟩ + b | 1 ⟩ , with a, b ∈ C and | a | 2 + | b | 2 = 1 . In QN, qubits cannot be copied and must therefore be transferred between remote nodes using quantum teleportation. This protocol relies on bipartite quantum entanglement, typically in the form of maximally entangled Bell states, | Φ ± ⟩ = 1 √ 2 ( | 00 ⟩ ± | 11 ⟩ ) and | Ψ ± ⟩ = 1 √ 2 ( | 01 ⟩ ± | 10 ⟩ ) , which form an orthonormal basis of two-qubit states. B. Quantum T eleportation Quantum teleportation enables the transfer of an unknown single-qubit state | ψ ⟩ from a source node (Alice) to a desti- nation node (Bob). W e consider teleportation assisted by an intermediate QR, as illustrated in Fig. 1. The protocol proceeds as follows: 1) Entanglement distribution via the QR: T wo Bell pairs are probabilistically generated by the QR. One Bell pair is distributed over the QR–Alice link, with one qubit stored in the quantum memory of the QR and the other stored at Alice. A second Bell pair is distributed ov er the QR–Bob link, with one qubit stored in the quantum memory of the QR and the other stored at Bob . Once both links succeed, the QR performs a Bell State Measurement (BSM) on its two stored qubits, realizing entanglement sw apping and establishing an ef fectiv e Bell pair shared between Alice (qubit A 1 ) and Bob (qubit B ). Alice also holds the input qubit A 0 , prepared in the state | ψ ⟩ . 2) BSM at Alice: Alice performs a joint BSM on qubits A 0 and A 1 , projecting them onto one of the four Bell states, destroying the original state of A 0 and mapping | ψ ⟩ onto Bob’ s qubit B up to a P auli byproduct operator . 3) Classical communication: The outcomes of the BSM operations at the QR and at Alice are encoded into classical bits and transmitted to Bob over a classical channel. 4) State reconstruction: Based on the receiv ed classical information, Bob applies the corresponding Pauli correction to qubit B , which deterministically recovers the state | ψ ⟩ . As a result of the required entanglement generation, swap- ping, and classical signaling operations, multiple qubits may remain stored in quantum memories at Alice, the QR, and Bob while awaiting protocol completion. During this storage time, interactions with the en vironment induce decoherence, progressiv ely degrading the corresponding quantum states ov er a characteristic time scale determined by the memory coherence time τ . I I I . S Y S T E M M O D E L W e consider the QN illustrated in Fig. 1, which consists of two remote nodes, i.e., Alice and Bob, interconnected through a QR. Alice and Bob host a distributed QApp that requires the teleportation of N qubit > 1 independent qubits from Alice to Bob . Each qubit n ∈ { 1 , . . . , N qubit } is teleported using a distinct Bell pair . Successful execution of the teleportation phase of the QApp requires that the fidelity of every teleported qubit satisfies F ( ρ ( n ) , ψ ( n ) ) ≥ F th . The QR manages parallel entanglement-generation attempts with Alice and Bob . Specifically , the QR is equipped with matter-based quantum memory of capacity 2 N par and coher- ence time τ QR , where N par denotes the maximum number of supported parallel entanglement-generation attempts. Success- fully generated qubits are buf fered in the quantum memory of the QR until the corresponding qubits on both links are av ailable for entanglement swapping. Entanglement generation is probabilistic and proceeds in discrete time slots of duration T slot = T comm + T att + T BSM + T PC . The term T comm = 2 d ′ /c accounts for round-trip classical signaling latency between the QR and a remote node, where d ′ denotes the QR–remote- node distance (with d ′ = d/ 2 assuming symmetric placement of the QR, and d the Alice–Bob separation), and c represents the propagation speed in the underlying transmission medium. The term T att corresponds to the duration of an entanglement- generation attempt. The term T BSM captures the time required to perform Bell-state measurements at the QR and at Alice. Finally , T PC accounts for the conditional Pauli corrections applied after classical information exchange. Entanglement generation and swapping follo w a standard heralded protocol. JOURN AL OF L A T E X CLASS FILES, V OL. X, NO. Y , MONTH YEAR 4 Fig. 2. A QN with tw o endpoints, connected either directly or via a QR, illustrating parallel entanglement distrib ution of N qubit qubits for a QApp with fidelity threshold F th . The entanglement distrib ution protocol considered follo ws the approach in [9]. In both scenarios, entanglement generation is probabilistic and proceeds in discrete time slots of fix ed duration T slot = T comm + T att , where T att denotes the duration of a single entanglement attempt and T comm = 2 d ef f /c accounts for the round-trip delay to transmit a photon o v er distance d ef f and recei v e the classical ackno wledgment from the BSM, with c being the speed of light in fiber . Here, d ef f n equals d for direct Alice–Bob links and d ′ when a QR is in v olv ed. The durations of l ocal operations in entanglement sw apping, BSM ( ≈ 10–100 ns) and conditional P auli corrections ( ≈ 10 ns), are se v eral orders of magnitude shorter than the entanglement generation times ( T comm + T att ) and are therefore ne glected in the slot duration. Furthermore, a multimode architecture is assumed, allo wing up to N par parallel Bell pair generation attempts per slot. Successful end-to-end entangled qubits are stored in local quantum memories with N qubit capacity at Alice and Bob, where the y are independently subject t o decoherence, char - acterized by coherence times τ A and τ B , r especti v ely , until consumed for teleportation. W e assume t h a t the QApp-le v el fidelity requirement F QApp th can be mapped to an equi v alent Bell-pair fidelity threshold F th , where this mapping depends on the specific technology and implementation emplo yed. The objecti v e is to accumulate N qubit Bell pairs in the local memories, each with fidelity at least F th . Once this condition is met, Alice generates the QApp qubits and transmits them to Bob via teleportation. A. Success Pr obability under Channel Losses W e relate ph ysical losses to entanglement generation prob- abilities. F or each qubit n ∈ N initially unentangled, Alice or the QR (depending on the scenario as illustrated in Fig. 2) prepares spin–photon entangled states | ψ ± n ⟩ = cos θ n | ↑ ⟩| 1 ⟩ ± sin θ n | ↓⟩| 0 ⟩ , where θ n determines the spin–photon entanglement. Photons are sent through independent optical fibers to their respecti v e recipients. The transmission ef ficienc y for each fiber is [24] η ( d ef f ) = P e P ce P det exp  − d ef f /L 0  , (1) accounting for emission probability P e , collection ef ficienc y P ce , detection ef ficienc y P det , and fiber attenuation length L 0 at the considered transmission w a v elength, which is identical for all fibers . Spin–spin entanglement is heralded by remote detections, with success probability [24] p suc = 2 η ( d ef f ) cos 2 ( θ n )  1 − η ( d ef f ) 2 cos 2 ( θ n )  . (2) B. Quantum Memory and Decoher ence Under depolarizing noise, the time e v olution of the den- sity matrix for a d -dimensional quantum sys tem is ρ n ( t ) = e − t/τ ρ n +  1 − e − t/τ  I d d , where τ is the characteristic co- herence time, ρ n is the initial state, and I d is the d -dimensional identity matrix. The first term represents the e xponentially decaying contrib ution of the initial state , while the second term models the transition to w ards the maximally mix ed state, which corresponds to complete loss of coherence. On the other hand, the fidelity between a quantum state ρ and an ideal pure state | ψ ⟩ is defined as F ( ρ, ψ ) = ⟨ ψ | ρ | ψ ⟩ , as discussed in Section II. Therefore, for a Bell pair , tw o qubits ( d = 2 ) each under going independent depolarizing noise in separate memories with coherence times τ A and τ B , the fidelity with respect to its initial non-ideal state, i.e., dif ferent to | Φ + ⟩ , | Φ − ⟩ , | Ψ + ⟩ , or | Ψ − ⟩ , and initial fidelity F 0 e v olv es as F ( t, t A , t B ) = 3 4 ·  4 · F 0 − 1 3  · e − ( t − t A ) τ A e − ( t − t B ) τ B + 1 4 , (3) where t A and t B denote the time instants when each qubit is stored in Alice’ s and Bob’ s quantum memories, respecti v ely . This e xpression reflects that fidelity decays e xponentially from 1 do wn to 0 . 25 , the latter corresponding to a fully mix ed tw o- qubit state. I V . A N A L Y S I S A N D M O D E L I N G O F Q A P P R E L I A B I L I T Y V I A Q U A R M A W e define the r eliability of a QApp, which depends on tw o main f actors: (i) the probabilistic nature of Bell-pair entanglement generation and storage attempts for each qubit, and (ii) the temporal decay of each qubit’ s fidelity due to decoher ence while stored in quantum memory . W e detail the computation of the o v erall and indi vidual probabilities in v olv ed in the r eliability analysis via Q U ARMA. A. Reliability of a QApp The r eliability R of a QApp with N qubit stored qubits is defined as the probability that all qubits simultaneously maintain a fidelity abo v e a tar get threshold F th at the time slot t last when the last qubit is successfully entangled and stored in quantum memory: R = P h T N qubit n =1 { F n ( t last ) ≥ F th } i . Fig. 1: A QN with two endpoints, connected via a QR, illustrating parallel Bell pair distribution of qubits. After entanglement swapping, the resulting end-to-end Bell pairs are stored in the local quantum memories of Alice and Bob, with capacities N qubit and coherence times τ A and τ B , respectiv ely . Each Bell pair is reserved for a single qubit and decoheres independently while stored. Qubits are teleported individually as soon as the corresponding Bell pairs become av ailable and are then stored in Bob’ s quantum memory , where decoherence starts upon successful teleportation. Let ρ ( q ) B denote the quantum state of qubit q stored at Bob after teleportation. The execution of the QApp is considered successful if, upon completion of the teleportation of the last qubit, the condition F ( ρ ( q ) B , ψ ( q ) ) ≥ F th holds for all q ∈ { 1 , . . . , N qubit } . If this condition is not satisfied, the QApp ex ecution is deemed unsuccessful and the entire teleportation procedure must be repeated, requiring the generation and consumption of a new set of N qubit Bell pairs. A. Quantum Channel Model W e consider two types of quantum channels for entangle- ment distribution between the QR and the remote nodes: Optical Fiber Links: Entanglement distribution is real- ized over optical fiber links using traveling photonic qubits. Each fiber supports a single entanglement-generation attempt, and parallelism is achie ved by deploying multiple fibers in parallel between the QR and Alice or Bob. Entanglement- generation attempts over dif ferent fibers are independent and non-interfering. Consequently , N par scales with the number of av ailable fiber links and is primarily limited by the deployed fiber infrastructure. T errestrial FSO Links: Entanglement distribution relies on line-of-sight FSO links, where parallel entanglement- generation attempts can be supported by transmitting multiple spatially separated optical beams between the QR and Alice or Bob. Each beam occupies a distinct spatial mode and is detected independently , enabling distinguishable and non- interfering entanglement-generation attempts [20]. The achiev- able parallelism N par is fundamentally constrained by the spa- tial degrees of freedom of the FSO channel, which are limited by the channel space–bandwidth product and practical factors such as beam di vergence, atmospheric turbulence, pointing accuracy , and receiv er aperture size. For realistic terrestrial links, these constraints restrict the number of independently addressable spatial modes to a finite range, typically satisfying 1 ≤ N par ≲ 10 [21]. B. Entanglement Success Pr obability W e first model the effecti ve transmission efficiency of the quantum links connecting the QR with Alice and Bob. For each link type, the effecti ve transmission efficiency is modeled as η ℓ = P e P det P ( ℓ ) ce C ℓ e − d ′ ℓ /L ℓ , (1) where ℓ ∈ { fiber , FSO } denotes the transmission medium and d ′ ℓ the corresponding physical link length. The term P e denotes the probability that a matter qubit emits a photon into the intended photonic mode at the transmitter , while P det denotes the probability that a photon arriving at the recei ver is successfully detected; both parameters capture intrinsic node- lev el efficiencies and are assumed to be independent of the transmission medium. The factor P ( ℓ ) ce accounts for coupling losses between the local photonic mode and the propagation mode of link type ℓ , including interface losses and, in the case of FSO links, residual ef fects such as pointing errors and turbulence-induced fading. The term L ℓ denotes the attenu- ation length associated with the corresponding transmission medium, capturing propagation losses along the link. For optical fiber links, i.e., ℓ = fiber, propagation occurs in a guided medium and geometric coupling losses are neglected, so we set C fiber = 1 . For FSO links, i.e., ℓ = FSO, propagation occurs over an unguided line-of-sight optical channel and geo- metric coupling losses are modeled using a truncated Gaussian beam model [22]. Specifically , the geometric coupling effi- ciency is giv en by C FSO = 1 − exp  −  2 a 2 FSO  /  w 2 [ d ′ FSO ]  , where a FSO = A FSO / 2 denotes the receiver aperture radius and w ( d ′ FSO ) is the beam radius at distance d ′ FSO . The latter is expressed as w ( d ′ FSO ) = w 0 q 1 + ( λd ′ FSO / ( π w 2 0 )) 2 , with w 0 denoting the beam waist at the transmitter and λ the optical wa velength. Giv en the ef fectiv e transmission ef ficiency η ℓ , the probabil- ity of successfully generating a heralded entangled state ov er link ℓ in a single attempt is modeled as [23] p ( ℓ ) suc = 2 η ℓ cos 2 θ  1 − η 2 ℓ cos 2 θ  , (2) where θ determines the matter–photon entanglement strength. C. Bell-P air F idelity Evolution under Memory Decoher ence As described in Section II-B, the teleportation protocol in volves multiple storage phases in which the qubits forming a Bell pair may temporarily reside in different quantum memories, including those of Alice, Bob, and the QR, each characterized by coherence times τ A , τ B , and τ QR , respec- tiv ely . Focusing on the generation of a Bell pair between two specific nodes during a single storage phase, we assume independent depolarizing noise acting on each stored qubit. Under this assumption, the fidelity of the Bell pair can be ev aluated over time t as F ( t, t 1 , t 2 ) = 3 4  4 F 0 − 1 3  e − t − t 1 τ 1 e − t − t 2 τ 2 + 1 4 . (3) where t 1 and t 2 denote the time instants at which the two qubits start being stored, and τ 1 and τ 2 are the corresponding memory coherence times, instantiated as τ QR , τ A , or τ B depending on the hosting nodes. The exponential terms model the independent coherence decay of each qubit. The af fine form ensures that the fidelity con verges to 1 / 4 for long storage times, corresponding to the ov erlap with a maximally mixed two-qubit state under depolarizing noise. The parameter F 0 denotes the Bell-pair fidelity immediately after its creation in the considered phase and captures imperfections introduced by entanglement generation and, when applicable, by entan- glement swapping. I V . R E L I A B I L I T Y O F M U LT I - Q U B I T T E L E P O RT AT I O N U N D E R F I D E L I T Y C O N S T R A I N T S This section introduces the reliability metric for multi-qubit quantum teleportation under fidelity constraints. The reliabil- ity captures the joint ef fect of multiple stochastic Bell-pair generation processes and the cumulativ e fidelity degradation experienced by qubits during successi ve storage phases in quantum memories throughout the teleportation protocol. A. Reliability Definition The reliability R captures the probability that the teleporta- tion of N qubit qubits is completed while all teleported qubits satisfy a target fidelity constraint. Let t last denote the time slot at which the last of the N qubit required Bell pairs has been suc- cessfully generated, distributed, and stored at Bob. The fidelity requirement is e xpressed as min n ∈{ 1 ,...,N qubit } F n ( t last ) ≥ F th , where F n ( t ) denotes the fidelity of the Bell pair associated with qubit n , ev aluated at time t . Since t last is a random variable, the reliability is obtained by av eraging over all possible completion times and is computed as R = T max X t last =1 P se [ t last ] R cond t last , (4) where P se [ t last ] denotes the probability that all N qubit Bell pairs have been successfully generated and stored by time slot t last , and R cond t last is the conditional probability that the fidelity constraint is satisfied at that time. Ideally , the summation would extend to infinity; in practice, T max is chosen such that P T max t last =1 P se [ t last ] ≥ 1 − ϵ , with ϵ a small tolerance (e.g., 10 − 6 ), ensuring that the neglected probability mass is negligible. B. Conditional Reliability at Completion T ime The conditional reliability R cond t last at completion time t last depends on the joint fidelity ev olution of the N qubit stored qubits and is giv en by R cond t last = P ( F ( t last ) ∈ F th ) , where F ( t last ) =  F 1 ( t last ) , . . . , F N qubit ( t last )  collects the fidelities of all Bell pairs at time t last and F th = { f : f n ≥ F th , ∀ n } denotes the feasible fidelity region. T o ensure tractability , we assume independent decoherence across qubits. This ap- proximation is reasonable in regimes where coherence is dominated by local noise sources, which is commonly the case in trapped-ion platforms [24] and solid-state quantum-network nodes such as NV centers [25]. Under this assumption, the conditional reliability factorizes as R cond t last = N qubit Y n =1 P fid [ n, t last ] , (5) where P fid [ n, t last ] denotes the probability that qubit n satisfies the fidelity constraint at time t last . C. F idelity Constr aints at Completion T ime The presence of an intermediate QR induces two indepen- dent entanglement-generation processes: one on the QR–Alice link (branch A ) and one on the QR–Bob link (branch B ). For a gi ven qubit n , entanglement generation on each branch succeeds at random time slots t A and t B with probabilities P A qubit [ n, t A ] and P B qubit [ n, t B ] , respectively . Once both pro- cesses succeed, entanglement swapping at the QR yields an end-to-end Bell pair shared between Alice and Bob. Due to the asynchronous completion of the two branches, the resulting Bell pair undergoes two consecuti ve storage phases before the completion time t last . The probability P fid [ n, t last ] that qubit n satisfies the fidelity constraint at completion time t last is obtained by av eraging ov er all possible entanglement-generation times ( t A , t B ) and is defined as P fid [ n, t last ] = t last X t A =1 t last X t B =1 P A qubit [ n, t A ] P B qubit [ n, t B ] 1 ( t A , t B ) t last X t A =1 t last X t B =1 P A qubit [ n, t A ] P B qubit [ n, t B ] , (6) where 1 ( t A , t B ) is an indicator function equal to 1 if the fidelity constraint is satisfied for the pair ( t A , t B ) , and 0 otherwise. The set of feasible pairs ( t A , t B ) is characterized by the following lemma. Lemma 1 (Storage-T ime Feasibility Condition) . Consider a qubit n for which entanglement generation on branches A and B succeeds at time slots ( t A , t B ) . The r esulting end-to-end Bell pair satisfies the fidelity constr aint F ( t last , t A , t B ) ≥ F th at completion time t last if and only if t ′ τ ′′ ( τ ′ + τ QR ) + t ′′ τ QR ( τ ′ + τ ′′ ) ≤  − τ QR τ ′ τ ′′ T slot ln  4 F th − 1 3  , (7) wher e t ′ = | t A − t B | , t ′′ = t last − max { t A , t B } , and ( τ ′ , τ ′′ ) = ( τ A , τ B ) if t A > t B , and ( τ ′ , τ ′′ ) = ( τ B , τ A ) otherwise. Pr oof: The fidelity at t last is deriv ed by considering two consecutiv e storage stages under the depolarizing noise model. In the first stage, of duration t ′ = | t A − t B | , entanglement is maintained on the branch that succeeded first; its fidelity F ′ is obtained by e valuating Eq. (3), i.e., F ′ = F ( t, t − t ′ · T slot , t − t ′ · T slot ) , with F 0 = 1 for a bipartite system with coherence times τ QR and τ ′ , where τ ′ corresponds to the first successful endpoint. Upon success of the second branch, entanglement swapping at the QR initializes the second storage stage. The final fidelity F ′′ at t last is then found by re-ev aluating Eq. (3) for an additional duration t ′′ = t last − max { t A , t B } , using F 0 = F ′ as the initial fidelity and ( τ ′ , τ ′′ ) as the endpoint coherence times. By enforcing the constraint F ′′ = F ( t, t − t ′′ · T slot , t − t ′′ · T slot ) ≥ F th on this cumulativ e ev olution and isolating the temporal variables via the natural logarithm, we obtain the reported feasibility condition. In this work, the probabilities P se [ t ] and P qubit [ n, t ] are obtained numerically using a Monte Carlo–based simulator . D. Monte Carlo Simulation Method The Monte Carlo simulator implements a single QR-assisted teleportation execution stage between Alice and Bob. T ime is discretized into slots of duration T slot . In each simulation run, entanglement-generation attempts are performed in parallel on the QR–Alice and QR–Bob links, with up to N par simultaneous attempts per slot. Each attempt succeeds or fails according to the stochastic entanglement-generation process defined in Section III-B. For each qubit, the simulator records the time slots ( t A , t B ) at which entanglement generation succeeds on the two branches and defines the completion time t last as the slot at which all N qubit required Bell pairs hav e been success- fully generated and swapped. Given the sampled values of ( t A , t B , t last ) , qubit fidelities at completion time are ev aluated according to the fidelity ev olution model introduced in Lemma 1. A simulation run is declared successful if all N qubit qubits satisfy the target fidelity constraint F th at completion time. Repeating this procedure over a large number of independent runs yields empirical estimates of P qubit [ n, t ] , P se [ t ] , and the resulting reliability R . T o facilitate reproducibility , the Python implementation of this Monte Carlo simulator is av ailable at [link to be made public upon manuscript acceptance] . V . E X P E R I M E N TA L S E T U P This section describes the experimental configuration used to assess the scalability of multi-qubit teleportation under fidelity and reliability constraints. A. P arameter Configur ation All experiments consider a single teleportation-based QApp ex ecuted between Alice and Bob with the assistance of one QR placed equidistantly between the two endpoints, which minimizes the maximum storage time of intermediate Bell pairs and is optimal from a fidelity perspective. Some system parameters are kept fixed across all exper- iments and are summarized in T able I. Transmission over both fiber and FSO links is assumed to operate at a common T ABLE I: Parameters used in the e xperimental e valuation. Parameter V alue Parameter V alue θ π / 4 [23] P e 0 . 6 [23] P det 0 . 85 [23] P ( fiber ) ce 0 . 9 [23] P ( FSO ) ce 0 . 8 [26] T att 5 . 5 µ s [23] T BSM 50 ns [23] T PC 10 ns [23] L fiber 21 . 7 km [27] L FSO 8 . 7 km [28] A FSO 0 . 20 m [29] λ 1550 nm [30] w 0 1 . 5 cm [31] T ABLE II: Coherence times τ for NV -center and trapped-ion quantum memory platforms. Platform Configuration / Conditions Coh. Times ( τ ) NV -Center High-purity , low 13 C, Cryogenic 1 – 3 ms [32] (Diamond) High-purity , Room T emp. (R T) 300 – 600 µ s [33] Near-surface, R T 10 – 100 µ s [34] High nitrogen concentration < 100 µ s [35] T rapped-Ion Optical : Passive memory a 100 – 500 ms [36] Ground-state Passi ve, no active suppression ∼ 10 – 60 s [37] (Hyperfine / W ith DD and SC b > 10 min [38] Clock) Activ e noise stabilization ∼ 1 . 5 h [39] a Limited by laser stability . b DD: Dynamical Decoupling; SC: Sympathetic Cooling. telecom wav elength λ = 1550 nm, and the reported node- lev el efficienc y parameters P e and P ( ℓ ) ce implicitly capture any interfacing required between the nativ e emission of the quantum memories and the optical communication channel. The remaining parameters define the experimental dimen- sions of the study . Specifically , the degree of parallelism is varied in the range N par ∈ [1 , 10] , the fidelity threshold is swept over F th ∈ [0 . 75 , 0 . 95] , and the target QApp reliability is set to R th ∈ [0 . 8 , 0 . 95] . F or each configuration, the number of qubits N qubit is progressi vely increased, and the maximum feasible v alue is identified as the largest N qubit satisfying R ≥ R th . B. Quantum Memory Coher ence T imes W e assume identical quantum-memory implementations at Alice, Bob, and the QR such that τ A = τ B = τ QR ≡ τ . This assumption av oids introducing node-dependent coherence- time heterogeneity and allows the analysis to focus on ho w a giv en memory coherence time τ affects QApp-lev el reliability , without loss of generality . The coherence time τ depends on the underlying quantum- memory platform and its operating conditions. W e follo w a technology-agnostic approach and instantiate τ using rep- resentativ e values reported for experimentally demonstrated quantum memories, considering solid-state spin qubits based on NV centers in diamond and atomic qubits implemented in trapped-ion systems. T able II summarizes representati ve v alues from the literature for both platforms. C. Experiments The experimental e valuation is organized into three exper - iments. Experiments 1 and 2 provide a parametric charac- terization of QApp-lev el reliability , focusing on the impact of parallel entanglement generation, end-to-end distance, and memory coherence time. W ithout loss of generality , these experiments consider fiber -based links and NV-center-based quantum memories. Experiment 3 then addresses the central question of this work, how many qubits can be teleported r eliably under fidelity constr aints in differ ent deployment sce- narios , by extending the analysis to heterogeneous settings in- cluding FSO links and trapped-ion-based quantum memories. The experiments are described belo w . Experiment 1: Reliability of Multi-Qubit Entanglement with Parallel Attempts. W e generate reliability performance curves for teleporting N qubit ∈ { 2 , 4 , 8 } qubits under fi- delity constraints. The fidelity threshold is swept over F th ∈ [0 . 75 , 1] , and the number of parallel entanglement-generation attempts over N par ∈ { 1 , 4 } . Discrete end-to-end distances d ∈ { 0 , 0 . 25 , 0 . 5 , 0 . 75 , 1 . 00 , 1 . 25 } km are considered. The memory coherence time is fixed to τ = 500 µ s . Experiment 2: Impact of Memory Coherence Time on Reliability . W e generate reliability performance curves as a function of the memory coherence time τ . The Alice–Bob distance is fixed to d = 1 . 5 km . The coherence time is swept ov er τ ∈ [10 µ s , 1 ms] . For each value of τ , reliability is 0 . 75 0 . 80 0 . 85 0 . 90 0 . 95 1 . 00 T arget Fidelit y ( F th ) 0 . 00 0 . 25 0 . 50 0 . 75 1 . 00 Reliabilit y ( R ) N qubits = 2 , N par = 1 0 . 75 0 . 80 0 . 85 0 . 90 0 . 95 1 . 00 T arget Fidelit y ( F th ) 0 . 00 0 . 25 0 . 50 0 . 75 1 . 00 Reliabilit y ( R ) N qubits = 4 , N par = 1 0 . 75 0 . 80 0 . 85 0 . 90 0 . 95 1 . 00 T arget Fidelit y ( F th ) 0 . 00 0 . 25 0 . 50 0 . 75 1 . 00 Reliabilit y ( R ) d = 0 . 00 km d = 0 . 25 km d = 0 . 50 km d = 0 . 75 km d = 1 . 00 km d = 1 . 25 km N qubits = 8 , N par = 1 0 . 75 0 . 80 0 . 85 0 . 90 0 . 95 1 . 00 T arget Fidelit y ( F th ) 0 . 00 0 . 25 0 . 50 0 . 75 1 . 00 Reliabilit y ( R ) N qubits = 2 , N par = 4 0 . 75 0 . 80 0 . 85 0 . 90 0 . 95 1 . 00 T arget Fidelit y ( F th ) 0 . 00 0 . 25 0 . 50 0 . 75 1 . 00 Reliabilit y ( R ) N qubits = 4 , N par = 4 0 . 75 0 . 80 0 . 85 0 . 90 0 . 95 1 . 00 T arget Fidelit y ( F th ) 0 . 00 0 . 25 0 . 50 0 . 75 1 . 00 Reliabilit y ( R ) N qubits = 8 , N par = 4 Fig. 2: Evaluation of reliability R with respect to the target fidelity F th . Note that τ = 500 µs . ev aluated for F th ∈ { 0 . 76 , 0 . 8 , 0 . 84 , 0 . 88 , 0 . 92 , 0 . 96 } , N qubit ∈ { 2 , 4 , 8 } and N par ∈ { 1 , 4 } . Experiment 3: Maximum Number of T eleportable Qubits. W e determine the maximum number of teleportable qubits N max qubit that can be supported under a target reliability R th as a function of the Alice–Bob distance d . The anal- ysis considers fiber -based and FSO links, and coherence- time regimes representati ve of NV-center-based and trapped- ion-based platforms. For each combination of link type and memory technology , feasibility regions in the ( d, N qubit ) plane are identified. The analysis considers parallelism lev els N par ∈ { 1 , 2 , 4 } and fidelity thresholds F th ∈ { 0 . 75 , 0 . 95 } , while all remaining parameters follow the configuration described in Section V -A. All experiments were executed on a machine equipped with 16 GB RAM and a quad-core Intel Core i7-7700HQ processor running at 2.80 GHz. V I . P E R F O R M A N C E R E S U LT S A. Experiment 1: Reliability of Multi-Qubit Entanglement with P arallel Attempts. Fig. 2 illustrates r eliability R as a function of the target fidelity F th for multiple combinations of N qubit and N par . First, increasing the number of qubits required by the QApp significantly reduces the r eliability . This is due to the joint nature of the success event over all N qubit Bell pairs and to the longer entanglement completion times, which amplify storage- induced decoherence. This is evident when comparing config- urations with different N qubit qubits. F or example, considering N qubit = 2 and N par = 1 , the r eliability at a target fidelity F th = 0 . 75 is R ≈ 1 for d = 250 m and R = 0 . 98 for d = 500 m . In contrast, for N qubit = 8 and N par = 1 , the r eliability drops to R = 0 . 2 at d = 250 m and to R = 0 . 1 at d = 500 m . Second, enabling parallel entanglement attempts has a substantial positi ve impact on system performance. This is e vident when comparing the top ro w ( N par = 1 ) to the bottom ro w ( N par = 4 ). Parallelism shortens the entanglement phase and limits the accumulated decoherence. In the previous example with N qubit = 8 , increasing N par from 1 to 4 allows the system to achieve unit r eliability for a target fidelity of F th = 0 . 85 when distances are lower than d = 500 m . B. Experiment 2: Impact of Memory Coher ence T ime on Reliability . Fig. 3 shows the resulting r eliability R as a function of the memory coherence time τ , for different combinations of N qubit ∈ { 2 , 4 , 8 } and N par ∈ { 1 , 4 } , and for different target fidelity values F th . The results show a clear trade-off between the number of qubits required by the QApp and the achie vable parallelism in the Bell-pair generation process. Increasing N qubit systemati- cally degrades the r eliability R , while higher parallelism N par mitigates this ef fect by reducing the effecti ve accumulation time. This follows from the joint success requirement ov er all N qubit Bell pairs and from the reduction of the completion time t last when parallel entanglement attempts are enabled. For instance, for N qubit = 8 and F th = 0 . 76 , R ≈ 0 . 45 N par = 1 when τ ≈ 1 ms , whereas N par = 4 raises the reliability to R ≈ 1 . In contrast, for short coherence times ( τ < 100 µ s ), QApps with N qubit = 8 and high parallelism exhibit R ≈ 0 . C. Experiment 3: Maximum Number of T eleportable Qubits Fig. 4 shows the maximum admissible Alice–Bob distance d max as a function of the target reliability R th for different values of N qubit , N par , F th , transmission media, and memory technology . For each configuration, the curves define the feasibility boundary beyond which R th cannot be sustained. For a fixed memory technology and R th , increasing the number of teleported qubits N qubit shifts the feasible operating region toward shorter distances. This is observed as a leftward 5 204 403 602 801 1000 Coherence Time ( τ ) [ µ s] 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 Reliability ( R ) N qubits = 2 , N par = 1 5 204 403 602 801 1000 Coherence Time ( τ ) [ µ s] 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 Reliability ( R ) N qubits = 4 , N par = 1 5 204 403 602 801 1000 Coherence Time ( τ ) [ µ s] 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 Reliability ( R ) N qubits = 8 , N par = 1 F th = 0 . 76 F th = 0 . 80 F th = 0 . 84 F th = 0 . 88 F th = 0 . 92 F th = 0 . 96 5 204 403 602 801 1000 Coherence Time ( τ ) [ µ s] 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 Reliability ( R ) N qubits = 2 , N par = 4 5 204 403 602 801 1000 Coherence Time ( τ ) [ µ s] 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 Reliability ( R ) N qubits = 4 , N par = 4 5 204 403 602 801 1000 Coherence Time ( τ ) [ µ s] 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 Reliability ( R ) N qubits = 8 , N par = 4 Fig. 3: Evaluation of reliability R with respect to the coherence time τ . Note that d = 1 . 5 Km. 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 T a r g e t r e l i a b i l i t y R t h N q u b i t = 1 N q u b i t = 2 N q u b i t = 3 N q u b i t = 4 N q u b i t = 5 N q u b i t = 1 N q u b i t = 2 N q u b i t = 3 N q u b i t = 4 N q u b i t = 5 N p a r = 2 , F t h = 0 . 7 5 N p a r = 2 , F t h = 0 . 8 N p a r = 2 , F t h = 0 . 8 5 5 11 22 46 98 205 431 906 1903 4000 M a x i m u m d i s t a n c e d m a x [ k m ] 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 T a r g e t r e l i a b i l i t y R t h F iber + NV center F iber + trapped ion F SO + NV center N p a r = 4 , F t h = 0 . 7 5 5 11 22 46 98 205 431 906 1903 4000 M a x i m u m d i s t a n c e d m a x [ k m ] N p a r = 4 , F t h = 0 . 8 5 11 22 46 98 205 431 906 1903 4000 M a x i m u m d i s t a n c e d m a x [ k m ] N p a r = 4 , F t h = 0 . 8 5 Fig. 4: Maximum achie vable distance d max as a function of the target reliability R th for NV -center-based memories with coherence time τ = 3 ms and for trapped-ion-based memories with coherence time τ = 250 ms . displacement of the feasibility boundary as N qubit increases, indicating a progressiv e reduction of distance d max . Comparing transmission media, optical fiber supports larger values of d max than terrestrial FSO for the same ( N qubit , R th ) pair , as sho wn by the fiber curves appearing to the right of the corresponding FSO curves. It is caused by the strong geometric coupling losses inherent to ground-based FSO links, which limit the achie vable distance e ven under clear -sky conditions. In the NV-center regime, FSO links yield feasible distances on the order of a few tens of kilometers whereas fiber -based links can sustain distances below 100 km depending on the reliability and fidelity targets. Memory technology has a dominant impact on the attainable distance scale. While NV-center-based memories are limited to short- and medium-range links, trapped-ion-based memories substantially expand the feasible regions. For fiber links, trapped-ion memories allo w d max values of sev eral hundreds of kilometers and, for N qubit = 1 , ev en beyond 1000 km . For terrestrial FSO links, feasible distances are inherently constrained by line-of-sight conditions and geometric coupling losses; in realistic ground-based scenarios, this typically limits operation to distances on the order of a few tens of kilometers ev en under fav orable conditions. For this reason, FSO config- urations with trapped-ion memories are not ev aluated. V I I . C O N C L U S I O N This paper studied the scalability of fidelity-constrained multi-qubit quantum teleportation between Alice and Bob, as- sisted by a single QR. W e introduced a QApp-le vel r eliability metric that captures the joint success of stochastic end-to- end Bell-pair generation, parallel entanglement attempts, and quantum-memory decoherence, and e valuated it via Monte Carlo simulation. Results show that memory coherence time is the dominant scalability bottleneck, while parallelism is essential to sustain reliability as the number of teleported qubits increases. Feasibility strongly depends on the underly- ing technology: NV-center-based memories restrict operation to short and medium distances, whereas trapped-ion-based memories enable reliable multi-qubit teleportation over hun- dreds of kilometers in fiber-based links, while terrestrial FSO links remain constrained by geometric coupling losses. Future work will focus on developing an analytical model to estimate the proposed reliability metric without relying on computationally intensive Monte Carlo simulations, enabling fast feasibility e valuation and system dimensioning for fidelity- constrained QApps. A C K N O W L E D G M E N T This w ork is part of grant PID2022-137329OB-C43 funded by MICIU/AEI/ 10.13039/501100011033 and by ERDF/EU. R E F E R E N C E S [1] S. W ehner, D. Elkouss, and R. Hanson, “Quantum internet: A vision for the road ahead, ” Science , vol. 362, no. 6412, p. eaam9288, 2018. [2] S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, “Fundamental limits of repeaterless quantum communications, ” Nat. Commun. , vol. 8, no. 1, p. 15043, 2017. [3] D. Bouwmeester, J. W . Pan, K. Mattle, M. Eibl, H. W einfurter , and A. Zeilinger , “Experimental quantum teleportation, ” Natur e , vol. 390, pp. 575–579, 1997. [4] B. Davies, T . Beauchamp, G. V ardoyan, and S. W ehner, “T ools for the Analysis of Quantum Protocols Requiring State Generation W ithin a T ime Windo w, ” IEEE T rans. on Quantum Eng. , vol. 5, pp. 1–20, 2024. [5] D. Main et al. , “Distrib uted quantum computing across an optical network link, ” Nature , vol. 638, pp. 383–388, 2025. [6] D. Barral et al. , “Revie w of Distributed Quantum Computing: From single QPU to High Performance Quantum Computing, ” Comput. Sci. Rev . , v ol. 57, p. 100747, 2025. [7] E. O. Ilo-Okeke, L. T essler, J. P . Dowling, and T . Byrnes, “Entanglement-based quantum clock synchronization, ” in AIP Conf. Pr oc. , vol. 2241, p. 020011, 2020. [8] M. Barhoumi, “Quantum-assisted network time synchronisation: A literature review , considering examples and challenges, ” SSRN Electr on. J. , 2024. [9] A. Pappa, A. Chailloux, S. W ehner , E. Diamanti, and I. Kerenidis, “Mul- tipartite Entanglement V erification Resistant against Dishonest Parties, ” Phys. Rev . Lett. , vol. 108, no. 26, p. 260502, 2012. [10] W . McCutcheon et al. , “Experimental V erification of Multipartite En- tanglement in Quantum Networks, ” Nat. Commun. , v ol. 7, p. 13251, 2016. [11] V . Krutyanskiy et al. , “T elecom-W avelength Quantum Repeater Node Based on a T rapped-Ion Processor, ” Phys. Re v . Lett. , vol. 130, p. 213601, May 2023. [12] W . Dai, T . Peng, and M. Z. Win, “Quantum Queuing Delay, ” IEEE J. Sel. Ar eas Commun. , vol. 38, no. 3, pp. 605–618, 2020. [13] G. V ardoyan, S. Guha, P . Nain, and D. T o wsley , “On the Exact Analysis of an Idealized Quantum Switch, ” P erform. Eval. , v ol. 144, p. 102141, 2020. [14] G. V ardoyan, S. Guha, P . Nain, and D. T o wsley , “On the Stochastic Analysis of a Quantum Entanglement Distribution Switch, ” IEEE T rans. on Quantum Eng. , vol. 2, pp. 1–16, 2021. [15] G. V ardoyan, P . Nain, S. Guha, and D. T owsley , “On the Capacity Region of Bipartite and Tripartite Entanglement Switching, ” A CM T rans. Model. P erform. Eval. Comput. Syst. , v ol. 8, Mar. 2023. [16] P . Nain, G. V ardoyan, S. Guha, and D. T o wsley , “On the Analysis of a Multipartite Entanglement Distribution Switch, ” Proc. A CM Meas. Anal. Comput. Syst. , vol. 4, June 2020. [17] N. K. Panigrahy , T . V asantam, D. T owsley , and L. T assiulas, “On the Capacity Region of a Quantum Switch with Entanglement Purification, ” in IEEE INFOCOM , pp. 1–10, 2023. [18] I. Tillman, T . V asantam, D. T owsle y , and K. P . Seshadreesan, “Calculat- ing the Capacity Region of a Quantum Switch, ” in IEEE QCE , vol. 01, pp. 1868–1878, 2024. [19] O. Bel and M. Kiran, “Simulators for quantum netw ork modeling: A comprehensiv e review, ” Comput. Netw . , vol. 263, p. 111204, 2025. [20] S. Koudia, L. Oleynik, J. ur Rehman, and S. Chatzinotas, “Spatial- mode div ersity and multiplexing for continuous variables quantum communications, ” Commun. Phys. , vol. 8, no. 351, 2025. [21] N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity limits of spatially multiplexed free-space communication channels, ” Nat. Photon. , vol. 9, no. 12, pp. 822–826, 2015. [22] S. Pirandola, “Limits and security of free-space quantum communica- tions, ” Phys. Re v . Res. , vol. 3, no. 1, p. 013279, 2021. [23] M. Chehimi, K. Goodenough, W . Saad, D. T owsley , and T . X. Zhou, “Entanglement Distrib ution Delay Optimization in Quantum Networks W ith Distillation, ” IEEE J . Sel. Areas Commun. , vol. 43, no. 5, pp. 1871– 1886, 2025. [24] C. D. Bruze wicz, J. Chia verini, R. McConnell, and J. M. Sage, “T rapped- ion quantum computing: Progress and challenges, ” Applied Physics Reviews , vol. 6, p. 021314, 05 2019. [25] C. E. Bradley et al. , “A T en-Qubit Solid-State Spin Register with Quantum Memory up to One Minute, ” Phys. Rev . X , vol. 9, p. 031045, Sep 2019. [26] A. S. El-W akeel, N. A. Mohammed, and M. H. Aly , “Free space optical communications system performance under atmospheric scattering and turbulence for 850 and 1550  nm operation, ” Appl. Opt. , vol. 55, pp. 7276–7286, Sep 2016. [27] A. Morana et al. , “Extreme Radiation Sensitivity of Ultra-Low Loss Pure-Silica-Core Optical Fibers at Low Dose Levels and Infrared W av e- lengths, ” Sensors , vol. 20, no. 24, p. 7254, 2020. [28] Z. K olka, D. Biolek, and V . Biolkov a, “Simulation of atmospheric optical channel with ISI, ” in CSECS , vol. 9, pp. 198–201, 2009. [29] H. Singh, N. Mittal, and K. A. Ogudo, “Optimizing the receiver aperture parameters of free space optical (FSO) link for performance enhancement, ” AIP Conf . Proc. , vol. 2495, p. 020030, 10 2023. [30] H. Kaushal and G. Kaddoum, “Optical Communication in Space: Challenges and Mitigation T echniques, ” IEEE Commun. Surv . T utor . , vol. 19, no. 1, pp. 57–96, 2017. [31] P . M. Lushniko v and N. Vladimirov a, “T o ward Defeating Dif fraction and Randomness for Laser Beam Propagation in T urbulent Atmosphere, ” JETP Lett. , vol. 108, no. 9, pp. 571–576, 2018. [32] G. Balasubramanian et al. , “Ultralong Spin Coherence Time in Isotopi- cally Engineered Diamond, ” Nature Mater . , vol. 8, pp. 383–387, 2009. [33] P . L. Stanwix et al. , “Coherence of nitrogen-vacancy electronic spin ensembles in diamond, ” Phys. Rev . B , vol. 82, p. 201201, Nov 2010. [34] S. Sangtawesin et al. , “Origins of Diamond Surface Noise Probed by Correlating Single-Spin Measurements with Surface Spectroscopy , ” Phys. Rev . X , vol. 9, p. 031052, Sep 2019. [35] T . Luo et al. , “Creation of nitrogen-v acancy centers in chemical v apor deposition diamond for sensing applications, ” New Journal of Physics , vol. 24, p. 033030, mar 2022. [36] C. Hempel, “T rapped-ion quantum computers, ” in Quantum T echnolo- gies. T rends and Implications for Cyber Defense (J. Jang-Jaccard, P . Caroff, E. Blezinger , V . Mulder, A. Mulder, and V . Lenders, eds.), pp. 15–24, Cham: Springer Nature, 2026. [37] T . P . Harty et al. , “High-fidelity preparation, gates, memory , and readout of a trapped-ion quantum bit, ” Phys. Rev . Lett. , vol. 113, p. 220501, Nov 2014. [38] Y . W ang et al. , “Single-qubit quantum memory e xceeding ten-minute coherence time, ” Nat. Photon. , vol. 11, no. 10, pp. 646–650, 2017. [39] P . W ang et al. , “Single ion qubit with estimated coherence time exceed- ing one hour, ” Nat. Commun. , vol. 12, p. 233, 2021.