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arXiv:2605.12130 · Physical Review A

Quantum teleportation with coherent error in Bell-state measurement

Jeonghyeon Shin, Jaehak Lee, Soojoon Lee, Seung-Woo Lee

quant-phSubmitted May 12, 2026• Announced May 13, 2026• 0 citations
v1 · May 12, 2026v2 · Oct 2, 2026
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Abstract

Quantum teleportation is a fundamental protocol in quantum information science, whose performance is conventionally evaluated under the assumption of ideal Bell-state measurements. In realistic implementations, however, joint measurements are often imperfect and can deviate from maximally entangled bases due to coherent errors in entangling operations. In this work, we analytically show how the entanglement of joint measurements determines teleportation performance and propose a strategy to overcome the limitations imposed by partially entangled joint measurements to recover the unit teleportation fidelity. We then derive an exact equation revealing a quantitative relation between measurement entanglement, channel entanglement, and the success probability to realize the unit-fidelity teleportation. We illustrate our results using elegant joint measurements and realistic coherent error models arising from imperfect entangling operations in quantum systems. Our work provides fundamental insight into the role of measurement entanglement in quantum teleportation and establishes a practical framework for achieving faithful teleportation without requiring substantial modifications to existing hardware.

Journal reference
Phys. Rev. A 114, 042401 (2026)
DOI
10.1103/py1h-hmn9
Comments
12 pages, 9 figures

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Quantum teleportation is a fundamental protocol in quantum information science, whose performance is conventionally evaluated under the assumption of ideal Bell-state measurements. In realistic implementations, however, joint measurements are often imperfect and can deviate from maximally entangled bases due to coherent errors in entangling operations. In this work, we analytically show how the entanglement of joint measurements determines teleportation performance and propose a strategy to overcome the limitations imposed by partially entangled joint measurements to recover the unit teleportation fidelity. We then derive an exact equation revealing a quantitative relation between measurement entanglement, channel entanglement, and the success probability to realize the unit-fidelity teleportation. We illustrate our results using elegant joint measurements and realistic coherent error models arising from imperfect entangling operations in quantum systems. Our work provides fundamental insight into the role of measurement entanglement in quantum teleportation and establishes a practical framework for achieving faithful teleportation without requiring substantial modifications to existing hardware.
In practical quantum communication, quantum channels are inevitably affected by noise and decoherence, leading to their degradation into non-maximally entangled or even mixed states. As a result, conventional quantum teleportation schemes based on non-maximally entangled channels are inherently probabilistic and cannot simultaneously achieve unit fidelity and unit success probability. To address this issue, we exploit the structural degrees of freedom of high-dimensional partially entangled channels and construct an asymmetric joint measurement basis matched to the Schmidt-coefficient distribution of the channel, thereby proposing a controlled multi-output perfect quantum teleportation scheme. First, based on a three-dimensional partially entangled five-qutrit channel, a controlled two-output teleportation model for unknown single-qubit states is established. Perfect transmission with both unit fidelity and unit success probability is achieved through the controller’s projective measurement, the sender’s asymmetric joint measurement, and the receivers’ corresponding local recovery operations. On this basis, the scheme is generalized to arbitrary d-dimensional partially entangled channels and further extended from the two-output configuration to the multi-output scenario. Our analysis shows that, when the two largest Schmidt coefficients of the channel are equal, deterministic perfect teleportation with both unit fidelity and unit success probability can still be achieved using non-maximally entangled resources. The proposed scheme is more consistent with realistic quantum communication environments and provides a theoretical foundation for efficient and controllable quantum information distribution in complex quantum networks.
Abstract Noiseless quantum channels are critical to share a pure maximally entangled state for performing an ideal teleportation protocol. However, in reality the shared entanglement severely degraded due to decoherence. In this paper, we propose a quantum teleportation channel protection scheme to enhance the teleportation fidelity in presence of decoherence. Before the entangled pair enters the decoherence channel, the weak measurement and flip operations are applied to transfer the qubit to a more robust state to the effects of the noise. After the decoherence channel the reversed flip operations and weak measurement reversal are applied to recover the initial state. We illustrate our protected teleportation scheme and compare it with a protocol based on weak measurement reversal. The numerical results show that the average teleportation fidelity of our proposed scheme can be significantly improved. Although the proposed entanglement protection scheme is probabilistic, after a successful entanglement transmission, we use the standard teleportation protocol which has probability one.
Abstract Quantum teleportation as the key strategy for quantum communication requires pure maximally shared entangled states among quantum nodes. In practice, quantum decoherence drastically degrades the shared entanglement during entanglement distribution, which is a serious challenge for the development of quantum networks. However, most of the decoherence control strategies proposed thus far are either resource-intensive or time-consuming. To overcome this obstacle, we enable noise-resistant teleportation through a noisy channel with a limited number of qubits and without applying time-consuming weak measurements. We apply a quantum gate control unit consisting of a controlled NOT gate and a rotation gate after the original teleportation protocol is accomplished. Furthermore, we demonstrate that a teleportation fidelity of unity is attainable when environment-assisted measurement is added to the proposed teleportation protocol via quantum gates. Moreover, we present an entanglement distribution process by employing the designed quantum gate control unit followed by the deterministic standard teleportation protocol to improve teleportation fidelity by establishing improved shared entanglement. Our performance analysis indicates that the proposed teleportation schemes offer a competitive fidelity and success probability compared with the conventional schemes and a recent weak measurement-based teleportation protocol.
Teleportation through a non-maximally entangled pair, e.g., ∣ψ(θ)⟩AB=cos⁡θ∣00⟩+sin⁡θ∣11⟩\ket{ψ(θ)}_{AB}=\cosθ\ket{00}+\sinθ\ket{11}∣ψ(θ)⟩AB​=cosθ∣00⟩+sinθ∣11⟩, induces a noisy channel and cannot achieve deterministic unit-fidelity transmission unless θ=π/4θ=π/4θ=π/4. We introduce a framework of \emph{assisted quantum teleportation} in which a third party (the ``Bank'') supplies auxiliary multipartite entanglement to restore a perfect Bell pair on the original ABABAB registers. We analyze two operational roles for the Bank: a Bank-measures model (measurement and broadcast) and a transfer model (the Bank transfers its subsystem and then leaves). For GHZ-class and W-class assistance we derive explicit feasibility regions for deterministic restoration and show an operational inequivalence for W resources. We further characterize finite-shot optimal success probabilities for probabilistic restoration and formulate Bank-measures feasibility for general pure Bank resources as a minimax optimization.
We introduce a generalized concept of quantum teleportation in the framework of quantum measurement and reversing operation. Our framework makes it possible to find an optimal protocol for quantum teleportation enabling a faithful transfer of unknown quantum states with maximum success probability up to the fundamental limit of the no-cloning theorem. Moreover, an optimized protocol in this generalized approach allows us to overcome noise in quantum channel beyond the reach of existing teleportation protocols without requiring extra qubit resources. Our proposed framework is applicable to multipartite quantum communications and primitive functionalities in scalable quantum architectures.
Quantum teleportation as a key protocol for quantum communication and quantum computing demonstrates the stark difference between quantum and classical information transmission. An ideal teleportation protocol requires pure maximally entangled state as the teleportation channel, while in real implementations the shared entanglement is severely degraded due to decoherence. In this letter, we propose a scheme to protect the quantum teleportation from decoherence by means of environment assisted measurement with weak measurements and flip operations. We show that the teleportation fidelity of our proposed scheme is significantly improved compared to teleportation with no protection and a teleportation protocol based on quantum measurement reversal. Also, the explicit formula of average teleportation fidelity and success probability of the entanglement protection are derived.