Teleportation-Based Transmission Efficiency

• Teleportation-based transmission efficiency is a metric that evaluates quantum state transfer by measuring fidelity, success probability, throughput, and resource overhead under noise and loss conditions.
• Advanced protocol designs employ entanglement engineering, ancillary and multiplexed methods to boost transmission rates and mitigate channel impairments.
• Robust performance across various architectures is achieved by optimizing loss resilience, resource allocation, and network design to meet scalable quantum communication demands.

Teleportation-based transmission efficiency quantifies the performance, resource utilization, and robustness of quantum-state transfer protocols that use quantum teleportation as their central communication or computation primitive. It encompasses the interplay between theoretical optimums, protocol-specific trade-offs, and physical constraints—such as noise, loss, and entanglement resources—in both discrete-variable (DV) and continuous-variable (CV) regimes, and across networked, long-distance, and local quantum architectures.

1. Definitional Scope and Fundamental Metrics

Teleportation-based transmission efficiency refers to the transmission rate, fidelity, and resource cost achievable in the transfer or distribution of quantum states using teleportation protocols, relative to both direct transmission and classical or classical-quantum hybrid communication strategies. Core metrics include:

• Fidelity ($F$): The overlap between the input quantum state and the teleported output, typically $$F = \langle\psi_{\rm in}| \rho_{\rm out} |\psi_{\rm in}\rangle$$.
• Success probability ($p_{\rm succ}$): The probability that the teleportation protocol yields a valid outcome.
• End-to-end throughput: The temporal density of successfully teleported quantum bits (qubits) or qudits per unit time or per use of a transmission channel.
• Resource overhead: The number and quality of resource states (entanglement consumption, ancillary modes, feedforward operations) per logical transmission.
• Robustness against loss and noise: Efficiency as a function of channel attenuation, operational infidelity, and decoherence.

Different settings (single-photon teleportation, CV protocols, hybrid and networked models) necessitate specialized definitions and optimization procedures.

2. Loss Models and Channel Attenuation Effects

Quantum teleportation fundamentally differs from direct quantum transmission in its sensitivity to channel losses and noise. Efficiency metrics become nontrivial when considering:

• Fixed-attenuation (e.g., optical fibers): For DV protocols (linear-optical), transmissivity $T = 10^{-L/10}$ directly modulates both transmission probability and fidelity. For example, Schrödinger-cat state CV teleportation loses nonclassicality beyond $\approx 5$ dB of fiber loss; the teleported state's fidelity—and its Wigner negativity—collapses at this threshold.
• Atmospheric-fading (free-space, satellite): Probabilistic models of turbulence (beam wandering, elliptic-beam deformation) yield distributions over transmissivities $T$, resulting in higher average fidelity for states subjected to strong but fluctuating losses. Satellite-based CV cat-state teleportation achieves $\bar{F}_{\rm sat}(30\,\mathrm{dB})\sim0.25$ (elliptic model), compared to $\sim0.05$ for fiber channels at the same mean loss (Do et al., 2019).
• Hybrid loss scenarios: Performance under spatial, spectral, and temporal multiplexing or in the presence of entangled ancilla networks is contingent on tailored error models.

Channel models thus not only determine the achievable fidelity per trial but fundamentally shape the viable operational regime for teleportation-based protocols.

3. Protocol Design and Resource Engineering

Transmission efficiency is intricately tied to the quantum resources and protocol design, including:

• Entanglement quality: Port-based teleportation (PBT) and its minimal variants achieve exponential suppression of teleportation failure probabilities at linear entanglement cost, with conditional fidelities $F=1-\mathcal{O}(1/N)$ for $N$ EPR pairs (Strelchuk et al., 2021).
• Ancilla and measurement enhancement: Linear-optical teleportation is limited to 50% Bell-state measurement (BSM) efficiency; ancillary states and cascaded interference can boost the unambiguous BSM rate to nearly 70%, with observed teleportation fidelities $F_{\rm boost}=0.8677\pm0.0024$ and acceptance rates $69.71\pm0.75\%$ (D'Aurelio et al., 7 Jun 2024).
• Multiport and multiplexed approaches: Multiport teleportation extends the one-shot capacity, allowing for nearly linear-in-$N$ multiplexed teleportation of qubits with approximate fidelity $F\sim1-\mathcal{O}(k/N)$, far exceeding standard PBT capacity scaling (Kopszak et al., 2020).
• Cooperative and controlled scenarios: Protocols designed to enable or restrict teleportation under controller authority (e.g., maximal-slice tripartite states) experience efficiency trade-offs according to loss, encoding (VSP vs coherent), and controllability (Medina et al., 2017).

Optimization across these axes is protocol-dependent, often invoking nontrivial measurement schemes (square-root measurements, generalized Bell/GHZ bases), dynamical ancilla management, and the use of tailored entangled states.

4. Transmission Rate, Capacity Scaling, and Multiplexing

Teleportation-based protocols can outperform naive single-channel transmission both in energy efficiency and rate, particularly via:

• Multiplexed CV protocols: For a total mean photon number $E$ over $N$ squeezed modes, teleportation capacity $C(E,N)$ achieves exponential scaling in $N$ at fixed $E$, provided per-mode squeezing exceeds a loss- and noise-dependent threshold $r_{\min}(\eta)$. Optimal $N\sim1.1E$ for lossless channels; multiplexing outperforms single-mode coding both in achievable rate and loss resilience (Christ et al., 2012).
• Superdense teleportation: Hyperentangled ququart SDT achieves high-dimensional deterministic transmission—a three-phase-encoded ququart per two classical bits—at per-shot fidelities $F\approx0.94$ and phase discrimination sufficient to guarantee transmission of $>10^5$ distinct states per LEO satellite pass (Chapman et al., 2019).
• Direct-vs-teleportation in microwaves: Microwave-optical quantum transduction via CV teleportation enables nonzero quantum capacity for arbitrarily small cooperativity $C$, while direct conversion requires $C\gtrsim0.17$ for positive capacity; teleportation consistently yields higher state-transfer fidelities and success rates for cat/GKP states in currently achievable hardware (Wu et al., 2023, Wu et al., 2021).

Efficiency ceilings are thereby dictated by bottlenecks in entanglement generation, BSM rate, and classical communication, as well as by physical constraints (channel loss, detector efficiency).

5. Efficiency Under Repeater and Networked Architectures

Teleportation enables increased reach and efficiency in distributed quantum architectures—provided resource allocation and protocol selection match network topology:

• Quantum repeaters: Standard entanglement-swapping necessitates maximally entangled resource states per segment to saturate optimal end-to-end fidelity. However, Ghosal et al. show that, for a class of noisy (rank-2) segments, identical link fidelities can be achieved with nonmaximal resource states (concurrence $C<1$), incurring strictly lower total ebit cost, $E_{\rm prop} = N C < N = E_{\rm std}$ (Ghosal et al., 20 Jun 2024).
• Teleportation-assisted routing in quantum algorithms: Replacing swap-path-based routing with teleportation-gate-assisted paths shortens the circuit depth from $O(d)$ to $O(1)$, achieving 10–25% reduction in benchmarked heavy-hexagon processors, at some cost in additional noise per teleported gate (Babu et al., 6 Feb 2025).
• Decentralized core interconnects: Two-way teleportation protocols halve the sequential communication hops required per inter-core transfer in mesh network architectures, realizing $\approx40\%$ reductions in communication latency and $\approx24\%$ reductions in compiled circuit depth compared to hop-by-hop baselines (S et al., 16 May 2025).
• Energy teleportation: Timelike Quantum Energy Teleportation (TQET), by harnessing temporal as well as spatial entanglement, increases extractable energy efficiency in spin chains from $\sim3\%$ in static QET to $\sim40\%$—a $>13\times$ improvement—demonstrating the ability of correlation-oriented protocol design to unlock new efficiency regimes (Ikeda, 7 Apr 2025).

These advances highlight the degree to which protocol and network engineering can extract untapped transmission efficiency from nonclassical channels.

6. Loss Resilience and Quantum-versus-Classical Performance Benchmarks

Teleportation offers quantifiable efficiency advantages over both direct quantum and optimal classical protocols, particularly in high-loss regimes:

• Photon-loss tolerance: Teleportation-based single-photon communication, using heralded entanglement and BSMs, can yield transmission probabilities $2.95\times$ greater than optimal classical strategies and $6.2\times$ that of direct transmission, with heralded entanglement efficiencies of 82% even after 15 dB of loss (Peng et al., 12 Nov 2025).
• Threshold performance: For port-based, multiport, and probabilistic protocols, explicit upper bounds for success rate versus entanglement quality are derived; for instance, direct teleportation using a partially entangled Bell state $|\Phi^+_n\rangle$ cannot exceed $P_{\rm max}=2n^2/(1+n^2)$ per trial (Fortes et al., 2012). This upper bound is saturable with composite protocols and careful ancilla correction.
• Analog-digital hybridizations: Analog quantum teleportation, leveraging a noisy quantum channel as feedforward, can outperform classical-feedforward (digital) schemes whenever the channel is not entanglement-breaking for the entanglement strength employed (Alushi et al., 14 Feb 2025).

Efficiency benchmarks are thus protocol-, resource-, and scenario-dependent, and they serve as both a tool for protocol certification and a design target for large-scale system deployment.

7. Protocol- and Application-Specific Trade-offs

Transmission efficiency is subject to context-dependent trade-offs:

• Fidelity-versus-success: Minimal port-based teleportation (mPBT) allows an exponential suppression of failure with only linear entanglement cost ($p_{\rm succ}=1-(N+2)/2^{N+1}$, $F=1-\mathcal{O}(1/N)$). In comparison, probabilistic PBT yields perfect fidelity at the expense of reduced (but analytically optimal) $p_{\rm succ}$ (Strelchuk et al., 2021).
• Resource allocation and classical communication: Multiplexed CV schemes require optimization of number of modes $N$ for given energy $E$ and channel transmissivity $\eta$; the protocol achieves maximal rate at $N_{\rm opt}\sim E$ and is loss-resilient provided per-mode squeezing exceeds $r_{\min}(\eta)$ (Christ et al., 2012).
• Operational complexity: Boosted teleportation using ancillary photonic states increases success rate, but requires matched spectral-temporal engineering and may introduce higher-order emissions and noise-tolerant error analysis (D'Aurelio et al., 7 Jun 2024).
• Security contexts: Teleportation-based CV-QKD protocols with known discrete input alphabets, optimized displacement, and adaptive parameters can maintain positive key rates at arbitrarily high optical loss, fundamentally bypassing the $\sim3$ dB loss limit in standard Gaussian modulated QKD (Luiz et al., 2014).

Such trade-offs define the operational envelope for practical deployments and guide future protocol improvements.

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Teleportation-based transmission efficiency thus represents a nuanced, protocol-specific, and context-sensitive measure of how well teleportation protocols convert entanglement and classical communication into robust, high-fidelity, and resource-efficient quantum state transfer under realistic constraints. It is maximized through a combination of loss modeling, resource optimization, multiplexing strategies, and the engineering of measurement and network protocols tailored to both physical platforms and target applications.