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arXiv:2510.13600 · Physical Review Applied

Quality assessment of quantum teleportation through the distribution of fidelity

Diego G. Bussandri, G. M. Bosyk, P. Crespo Del Amo, Karol Życzkowski

Published May 19, 2026• 0 citations
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Abstract

In this work, we introduce a comprehensive statistical framework for assessing single-qubit quantum teleportation performance beyond the conventional average-fidelity benchmark. At first, we derive a closed-form expression for the full probability density function of actual teleportation fidelities and apply it to both classical measure-and-prepare schemes and standard quantum teleportation, considering two relevant noise models: Bell-diagonal resource states and local amplitude-damping channels. These results reveal that protocols with identical average fidelities can exhibit markedly different statistical behaviors, and that relying solely on average fidelity can mask inherent asymmetries introduced by local noise, potentially leading to spurious conclusions of symmetry. Secondly, we introduce a certification method based on prior importance functions (e.g., Beta distributions), which unifies moment-based criteria and threshold-based success probabilities into a single figure of merit. Applying this framework, we show that certifying high-fidelity teleportation requires increasingly stronger entanglement or non-locality, and we clarify that the so-called ``fighting noise with noise'' effect arises from the chosen prior importance function rather than representing a genuine advantage. Our approach thus provides versatile tools for tailored, application-specific teleportation benchmarks.

DOI
10.1103/3gvb-qqx1

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In this work, we introduce a comprehensive statistical framework for assessing single-qubit quantum teleportation performance beyond the conventional average-fidelity benchmark. At first, we derive a closed-form expression for the full probability density function of actual teleportation fidelities and apply it to both classical measure-and-prepare schemes and standard quantum teleportation, considering two relevant noise models: Bell-diagonal resource states and local amplitude-damping channels. These results reveal that protocols with identical average fidelities can exhibit markedly different statistical behaviors, and that relying solely on average fidelity can mask inherent asymmetries introduced by local noise, potentially leading to spurious conclusions of symmetry. Secondly, we introduce a certification method based on prior importance functions (e.g., Beta distributions), which unifies moment-based criteria and threshold-based success probabilities into a single figure of merit. Applying this framework, we show that certifying high-fidelity teleportation requires increasingly stronger entanglement or non-locality, and we clarify that the so-called ``fighting noise with noise'' effect arises from the chosen prior importance function rather than representing a genuine advantage. Our approach thus provides versatile tools for tailored, application-specific teleportation benchmarks.
The conventional certification method for quantum teleportation protocols relies on surpassing the highest achievable classical average fidelity between target and teleported states. Our paper highlights the limitations of this approach: inconsistent conclusions can be obtained when considering different distance measures in the quantum state space, leading to contradictory interpretations. In particular, this behavior is manifested when modeling a very common noisy experimental scenario, in which the resource state takes the form of a Werner state generated by the influence of a depolarizing channel acting on the Bell state resource. Two additional noise models, based on amplitude-damping channels, are also analyzed. Our paper, therefore, stresses the necessity of new certification methods for quantum teleportation.
We develop a unified framework to analyze ddd-dimensional quantum teleportation through the joint geometry of two complementary figures of merit: average fidelity FFF (how well a protocol works on average) and fidelity deviation DDD (how uniformly it works across the inputs). Technically, we formulate a representation-theoretical framework based on Schur-Weyl duality and permutation symmetry calculus that reduce the higher-moment Haar averages to a finite set of trace invariants of the composed correction unitaries. This yields closed-form expressions for FFF and DDD in arbitrary Hilbert-space dimension and delivers tight bounds that link the admissible deviation directly to the gap from the optimal average performance. In particular, any measured pair (F,D)(F, D)(F,D) can be ported into a visibility estimate for isotropic channel resources, turning the (F,D)(F, D)(F,D)-plane into a calibrated diagnostic map. We further cast the teleportation advantage and CGLMP-inequality violation as two witnesses lines in the (F,D)(F,D)(F,D) plane: one line certifies that FFF beats the classical benchmark 2/(d+1)2/(d{+}1)2/(d+1), while the other line certifies the Bell nonlocality. Their identical slope but distinct intercepts expose a quantitative gap between "entangled yet local" and "genuinely nonlocal" resources.
Quantum teleportation, a cornerstone of quantum information science, enables the transfer of an unknown quantum state from one location to another without physically moving the state itself. Its efficacy is primarily quantified by fidelity, a measure of how closely the teleported state resembles the original. Achieving high-fidelity teleportation is paramount for practical applications in quantum communication and computation. This paper explores the intricate relationship between non-locality, the no-cloning theorem, and the pursuit of high-fidelity quantum teleportation. We introduce the concept of "unclonable non-locality" to describe scenarios where the inherent non-local correlations of entangled states are leveraged in a manner that inherently resists illicit copying, thereby enhancing the integrity and security of the teleportation process. We review current state-of-the-art teleportation protocols, analyzing their fidelity limitations and the impact of various noise models, such as those arising from Bell-diagonal resource states and local amplitude-damping channels. Our framework emphasizes that protocols exhibiting identical average fidelities can conceal distinct statistical behaviors and asymmetries introduced by local noise, stressing the need for a comprehensive statistical assessment beyond simple average fidelity. We propose methods for constructing and utilizing entangled resources that maximize non-local correlations while inherently enforcing the no-cloning principle, thereby offering a robust pathway to deterministic, high-fidelity quantum state transfer. The discussion highlights the potential for designing tailored teleportation benchmarks based on prior importance functions, unifying moment-based criteria and threshold-based success probabilities into a single figure of merit, and clarifying the role of entanglement strength in certifying high-fidelity teleportation. We also acknowledge the ethical implications associated with the development of powerful quantum technologies that could have significant societal impacts.
Quantum teleportation should surpass maximum fidelity thresholds possible with local measurements and classical communications. Benchmarks have been established when states are drawn from a uniform distribution of qubits or coherent states of harmonic oscillators. These are not applicable when there is prior knowledge about the input that skews the distribution. We determine the highest mean fidelity achievable for teleportation of states without using entanglement but drawn from a non-uniform prior distribution, specifically a von Mises - Fisher distribution. Using Bayesian methods, we derive benchmark functions for single qubit teleportation that utilize projective measurement on specific axes on the Bloch sphere. We demonstrate that similar results can be achieved with a coherent spin positive operator-valued measure (POVM), based upon heterodyne detection. These methods are then used to derive corresponding benchmarks for teleporting multi-qubit systems that we model as spin coherent states, covering the full range of particle number N∈[1,∞)N\in [1, \infty)N∈[1,∞). The results show that fidelity thresholds to declare quantum advantage can be significantly higher than is typically assumed with uniform distribution.
Continuous-variable (CV) quantum teleportation is usually benchmarked by average fidelity, but when the teleportation is repeatedly used within optical networks or measurement-based architectures, uniformity across the input ensemble becomes equally important. We analyze this issue using two complementary figures of merit: the average fidelity and the fidelity deviation, which quantifies the input dependence of the single-shot teleportation fidelity. We prove that any deterministic unity-gain teleportation channel that is displacement covariant has vanishing fidelity deviation for coherent-state benchmarking, irrespective of whether the shared entangled resource is Gaussian or non-Gaussian. Nonzero deviation therefore diagnoses covariance breaking rather than non-Gaussianity. We then show that when a protocol raises the average fidelity through input-selective conditioning, the deviation generically increases in tandem, giving a quantitative universality cost. As a concrete example, we study teleportation enhanced by the so-called measurement-based noiseless linear amplification, where a heralded filter acts on the Bell-measurement record. The resulting trade-off among average fidelity, fidelity deviation, and success probability shows that stronger filtering can improve the conditional fidelity only by concentrating the successful events in favored regions of phase space, thereby suppressing the success probability and reducing input uniformity. Our results provide an operational framework for distinguishing genuine channel improvement from selectivity-driven post-selected advantage and suggest that the probabilistic CV teleportation should be assessed with average quality, universality, and heralding rate treated on an equal footing.
Developing reliable methods for certifying the dimension of a given quantum system or process is essential to ensure the validity of claimed realization of high-dimensional (HD) quantum advantages. The existing criteria for certifying genuine HD quantum teleportation (HDQT) mainly focus on demonstrating the successful transmission of genuine HD quantum states. However, a complete certification of HDQT must also identify the entanglement dimension of resource, which is critical for verifying whether the transmission capacity and noise resilience meet the necessary thresholds. Here we propose two universal criteria (based on fidelity and robustness, respectively) for certifying genuine HDQT behaviors that can close this gap by fully identifying the dimension of the entanglement. Both criteria require only the input and output teleportation data and remain feasible under partial Bell-state measurements. Furthermore, the robustness-based criterion has stronger noise resistance and it requires no prior assumptions about local operations, making it robust even in black-box scenario. Our results establish a universal and reliable theoretical framework for validating the core quantum advantage in HDQT, pivotal for ensuring the reliable links in HD quantum networks.