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arXiv:2310.09851 · Physical Review A

Robust quantum teleportation via a non-Markovian channel

Yanfang Wang, Shibei Xue, Hongbin Song, Min Jiang

Published Dec 8, 2023• 15 citations
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Abstract

In this paper we propose a non-Markovian quantum channel approach to mitigating the degradation of the average fidelity in continuous-variable quantum teleportation. The non-Markovian quantum channel is modeled by an augmented system where ancillary systems are introduced to represent the internal modes of non-Markovian environments. With a proper non-Markovianity, enhanced effects of the channels on continuous-variable quantum teleportation are observed. Also, the logarithmic negativity of entangled states can be effectively maintained so that the decay of the average fidelity of quantum teleportation is mitigated. In addition, the analysis on different teleported quantum states shows that coherent states exhibit stronger robustness than those of squeezed states and cat states in quantum teleportation with a non-Markovian channel.

DOI
10.1103/physreva.108.062406

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•Aug 28, 2026•0 citations
In this paper we propose a non-Markovian quantum channel approach to mitigating the degradation of the average fidelity in continuous-variable quantum teleportation. The non-Markovian quantum channel is modeled by an augmented system where ancillary systems are introduced to represent the internal modes of non-Markovian environments. With a proper non-Markovianity, enhanced effects of the channels on continuous-variable quantum teleportation are observed. Also, the logarithmic negativity of entangled states can be effectively maintained so that the decay of the average fidelity of quantum teleportation is mitigated. In addition, the analysis on different teleported quantum states shows that coherent states exhibit stronger robustness than those of squeezed states and cat states in quantum teleportation with a non-Markovian channel.
We study the continuous-variable (CV) quantum teleportation protocol in the case that one of the two modes of the shared entangled resource is sent to the receiver through a Gaussian Quantum Brownian Motion noisy channel. We show that if the channel is engineered in a non-Markovian regime, the information backflow from the environment induces an extra dependance of the phase of the two-mode squeezing of the shared Gaussian entangled resource on the transit time along the channel of the shared mode sent to the receiver. Optimizing over the non-Markovianity dependent phase of the squeezing yields a significant enhancement of the teleportation fidelity. For short enough channel transit times, essentially unit fidelity is achieved at realistic, finite values of the squeezing amplitude for a sufficiently large degree of the channel non-Markovianity.
We investigate quantum teleportation of a single unknown qubit state for the dissipative situation in which both qubits of the entangled channels that are formed by the pure and mixed maximally entangled states are subjected to local structured reservoirs. We consider the dissipative factors in Markovian and non-Markovian regimes on the average fidelity of the teleportation by solving the quantum master equation. It is shown that the fidelity of teleportation decreases exponentially over time in Markovian environments and attenuates oscillatorily in non-Markovian ones. In addition, when the non-Markovian and detuning conditions are satisfied simultaneously, the fidelity increases as the detuning increases. Even with a lower purity of entanglement, fidelity can be preserved effectively at comparatively high levels.
We investigate the fidelity and the linear entropy of teleportation using a shared two qubit initially maximally entangled state as a quantum channel, in which one qubit interacts with a two-state system named as the probe particle in a reservoir by dispersive atom-field coupling. Without the coupling of the probe particle with the reservoir, the quantum channel state is a pure state but not an initially maximally entangled state under the influence of the probe particle, and thus Bob obtains a pure state with an average fidelity fluctuating between 2/3 and 1 with time t. In the cases of the probe particle coupling with the reservoir the Markovian and non-Markovian dynamics of such a quantum channel are discussed in detail to show the influence of the reservoir on teleportation. The quantum channel state is a mixed state, but its entanglement does not die under the influence of the reservoir. It is found that, for a given teleported state, the fidelity and the linear entropy both evolve asymptotically to their fixed values, respectively, which are relative to the decay rate γ (Markovian) or to the pseudomode decay rate Γ (non-Markovian). Furthermore, when time t ≫ γ^(-1) and t ≫ Γ^(-1), the average fidelity increases with the augments of γ and Γ, while it decreases with the aggrandizement of the dispersive interaction strength κ.
Summary form only given. An unknown continuous-variable state can he teleported by use of the two-mode squeezed state as the quantum channel. If the quantum channel is maximally squeezed (100% squeezing), the unknown state will be perfectly reproduced at a remote place. However the assumption of the maximally squeezed quantum channel is unphysical as it means the infinite average photon number of the channel state. Moreover, the interaction of the channel state with the environment degrades the entanglement and purity of the channel. We are interested in how the nonclassical features of the unknown state is revived by quantum teleportation in the real world. It is obvious that a nonclassical nature in the unknown state can be lost during the teleportation even when the channel is entangled unless it is maximally entangled Is it also obvious that any nonclassical feature, cannot be teleported by a classical correlated channel? We find the relation between the entanglement of the channel and teleportation of nonclassical nature in the unknown state.
Preserving entanglement during the teleportation of multipartite quantum states is a central challenge in continuous-variable quantum communication, particularly when experimentally feasible finite-dimensional entangled resources are employed. In this work, we investigate whether the entanglement of a two-mode continuous-variable state can be preserved when only one of its modes is teleported through a multimode interferometry-based protocol using a three-dimensional discrete entangled channel. Two representative entangled states, namely the two-mode squeezed vacuum and discrete-modulation states, are considered under both ideal conditions and four standard quantum noise channels: bit-flip, phase-flip, depolarizing, and amplitude-damping. The protocol is evaluated in terms of teleportation fidelity, success probability, logarithmic negativity, Wigner-function evolution, and state purity to provide a comprehensive assessment of both teleportation quality and entanglement preservation. The results show that, in the absence of noise, the protocol preserves most of the initial entanglement while maintaining high teleportation fidelity. Under noisy conditions, the residual entanglement remains remarkably robust against amplitude-damping and phase-flip noise, whereas bit-flip noise causes the most pronounced degradation. The phase-space structure and purity of the teleported states are likewise largely retained over a broad range of noise strengths. These findings demonstrate that multimode interferometry with finite-dimensional entangled channels provides an effective and noise-resilient approach for preserving continuous-variable entanglement during quantum teleportation, offering a practical route toward realistic quantum communication networks.