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Physical Review A

Enhancing quantum teleportation with continuous-variable cluster states via photon subtraction

Mingjian He, Shouyin Liu

Published Oct 6, 2025• 2 citations
Publisher

Abstract

Quantum teleportation using continuous-variable cluster states is a promising method for quantum state transmission. Experiments show photon subtraction improves the fidelity of two-mode-entangled state-based teleportation, but its effect on universal quantum teleportation with cluster states is unclear. This study clarifies this issue. We create a characteristic function-based representation for universal teleportation, combining it with the Hermite polynomial representation to analyze the impact of photon subtraction. Our analysis finds that the enhancement depends on the photon subtraction modes and the initial squeezing parameter of cluster states. Contrary to the two-mode case, subtracting photons from all cluster state modes does not improve fidelity. By analyzing the equivalent squeezing of initial states after photon subtraction, we determine that squeezing improvement decides teleportation quality. A remarkable finding reveals that performing photon subtraction on two modes of a multirail cluster state can enhance equivalent squeezing of all modes, offering new possibilities for quantum information processing tasks.

DOI
10.1103/1jvj-r27q

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Quantum teleportation using continuous-variable cluster states is a promising method for quantum state transmission. Experiments show photon subtraction improves the fidelity of two-mode-entangled state-based teleportation, but its effect on universal quantum teleportation with cluster states is unclear. This study clarifies this issue. We create a characteristic function-based representation for universal teleportation, combining it with the Hermite polynomial representation to analyze the impact of photon subtraction. Our analysis finds that the enhancement depends on the photon subtraction modes and the initial squeezing parameter of cluster states. Contrary to the two-mode case, subtracting photons from all cluster state modes does not improve fidelity. By analyzing the equivalent squeezing of initial states after photon subtraction, we determine that squeezing improvement decides teleportation quality. A remarkable finding reveals that performing photon subtraction on two modes of a multirail cluster state can enhance equivalent squeezing of all modes, offering new possibilities for quantum information processing tasks.
Continuous-variable (CV) gate teleportation using cluster states is a cornerstone of quantum information processing. However, its performance is constrained by technical hurdles in preparing high-quality squeezed states, which are a critical resource for CV quantum protocols. Imperfect preparation of these squeezed states introduces noise, which in turn degrades quantum correlations. Photon subtraction has been shown to mitigate the adverse effects of imperfect squeezing by enhancing the equivalent squeezing of quantum resources. Accordingly, this study investigates the application of photon subtraction in CV gate teleportation. We first present a Wigner characteristic function representation for the two-mode quantum non-demolition gate teleportation protocol. Building on this representation, we establish a theoretical model incorporating photon subtraction, derive expressions for the fidelity and log-negativity of the output states, and verify the system performance through numerical simulations. Our results demonstrate that photon subtraction can effectively compensate for the losses both in fidelity and entanglement caused by imperfect squeezed states. In contrast to standard state teleportation based on two-mode entangled resources, such an enhancement is only achievable when photon subtraction is implemented prior to the generation of the final cluster state. This discovery represents a crucial practical advancement in the field of quantum teleportation, potentially paving the way for more efficient and reliable quantum communication systems.
We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced for any squeezing parameter rrr and these enhancements increase with the number of subtracted photons in the low-squeezing regime, while asymmetric multiple-photon subtractions will generally reduce these quantities. For the multiple-photon-added TMSVs, although it holds stronger entanglement, its EPR correlation, two-mode squeezing, sum squeezing, and the fidelity of a coherent state are always smaller than that of the TMSVs. Only when considering the case of teleporting a squeezed vacuum state does the symmetric photon addition make somewhat of an improvement in the fidelity for large-squeezing parameters. In addition, we analytically prove that a one-mode multiple-photon-subtracted TMSVs is equivalent to that of the one-mode multiple-photon-added one. And one-mode multiple-photon operations will diminish the above four quantities for any squeezing parameter rrr.
We consider non-Gaussian states generated by photon subtraction (PS) and photon addition (PA) on two-mode squeezed coherent (TMSC) states as resource states for continuous variable quantum teleportation. To this end, we derive the Wigner characteristic function for the family of photon-subtracted and photon-added TMSC states, which is then utilized to calculate the fidelity of teleporting a single-mode coherent state and a squeezed vacuum state. The analysis shows that, while symmetric PS enhances the fidelity of teleportation in an extensive range of squeezing, asymmetric PS enhances the performance marginally and only in the low squeezing regime. The addition operations, however, are less useful, symmetric three-PA leads to a marginal improvement while the other addition operations are useless. We consider the actual experimental setup for PS and PA operations and compute their success probabilities, which should be kept in mind while advocating the use of these operations. We could compute the fidelity of teleportation for a broad range of states because we analytically derive the Wigner characteristic function for these family of states, which we think will be useful for various other applications of these families of states.
Quantum state engineering frequently employs non-Gaussian operations, particularly photon addition and subtraction, to tailor and improve the nonclassical characteristics of quantum states. We investigate how photon addition to a two-mode squeezed Fock state (TMSFS) influences its performance in the Braunstein-Kimble quantum teleportation protocol. We obtain the Wigner characteristic function of the photon-added TMSFS (PA-TMSFS) and evaluate the corresponding teleportation fidelities for both Gaussian and non-Gaussian input states. We further compare the teleportation performance of PA-TMSFS with that of its photon-subtracted counterpart by accessing their fidelity enhancements over the parent TMSFS and considering the probabilistic nature of both the operations. Our results demonstrate that photon subtraction provides superior teleportation performance compared with photon addition, with this advantage becoming more pronounced when the success probabilities of the corresponding non-Gaussian operations are considered. In particular, the symmetric (1,1)(1,1)(1,1) photon subtraction yields the optimal trade-off between teleportation fidelity and success probability among the configurations investigated. These findings highlight that photon subtraction retains its advantage even when the underlying entangled resource is already non-Gaussian.
In this work, we investigate the performance of non-Gaussian entangled resources in continuous-variable quantum teleportation within a realistic setting. We describe the characteristic functions of three distinct entangled resources, a two-mode squeezed vacuum state, a two-mode photon-subtracted squeezed state, and a two-mode photon-added squeezed state. We extend the theoretical analysis by Yang et al. to include the realistic experimental conditions such as photon losses, imperfect measurements which typically affect continuous-variable quantum teleportation. Our results demonstrate that even in non-ideal situations, the photon-subtracted squeezed state outperforms the other two resources in the low squeezing regime, keeping fidelity above the classical threshold that suggests the robustness of photon-subtracted squeezed state in practical teleportation applications. We further analyze the EPR correlations of these entangled resources, revealing that the photon-subtracted squeezed state exhibits stronger EPR correlations than the original two-mode squeezed vacuum state and the two-mode photon-added squeezed state. This study merges theoretical models with realistic imperfections and utilizes non-Gaussian entanglement into high-fidelity quantum teleportation.
We present a detailed phase-space analysis of continuous-variable quantum teleportation using a photon-subtracted two-mode squeezed Fock state (PS-TMSFS) as an entangled resource. We investigate the performance of PS-TMSFS within the Braunstein-Kimble teleportation protocol. The resource-state preparation is described and the success probability related to the photon-subtraction process is derived analytically. The Wigner characteristic function of PS-TMSFS is calculated and then employed to determine the fidelity for input Gaussian and non-Gaussian states. The dependence of the success probability and the teleportation fidelity on the squeezing parameter and the beam-splitter transmissivity is analyzed for both symmetric and asymmetric photon-subtraction scenarios. This results that the symmetric photon subtraction consistently outperforms the corresponding asymmetric configurations with the (2,2)(2,2)(2,2) configuration providing the highest teleportation fidelity among the considered PS-TMSFS resources. A significant improvement over the Gaussian two-mode squeezed vacuum (TMSV) resource is observed for teleporting Gaussian input states, particularly in the low-squeezing regime, whereas the relative advantage for non-Gaussian input states depends on the functioning resource parameters and gradually diminishes as squeezing increases.