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arXiv:2210.00238 · International Journal of Quantum Information

Incompatibility of optimized protection of entanglement and teleportation fidelity in the presence of decoherence

Priyanka Chowdhury

Published Oct 17, 2025• 0 citations
arXivHTMLPDF

Abstract

Entanglement is the key to teleport an unknown quantum state with fidelity higher than classical limit. For decohering open quantum systems, entanglement decreases with the strength of interaction between quantum systems and the environment. As a result, teleportation fidelity decreases. The technique of weak measurement and its reversal help to protect entanglement in the presence of amplitude-damping decoherence. In this work, we have shown that the optimal protection of entanglement measured by concurrence does not always optimize teleportation fidelity in the presence of decoherence modeled by the amplitude damping decoherence. More specifically, when one of the systems interacts with the environment, optimization of entanglement and teleportation fidelity requires different strengths of reverse weak measurement. Here, the success probability of optimal protection of entanglement is higher than the success probability of optimal protection of teleportation fidelity. Interestingly, when both systems interact with the environment, optimization of entanglement implies optimization of teleportation fidelity. Therefore, the resources of quantum teleportation along with entanglement need to be explored.

DOI
10.1142/s0219749925500327

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Entanglement is the key to teleport an unknown quantum state with fidelity higher than classical limit. For decohering open quantum systems, entanglement decreases with the strength of interaction between quantum systems and the environment. As a result, teleportation fidelity decreases. The technique of weak measurement and its reversal help to protect entanglement in the presence of amplitude-damping decoherence. In this work, we have shown that the optimal protection of entanglement measured by concurrence does not always optimize teleportation fidelity in the presence of decoherence modeled by the amplitude damping decoherence. More specifically, when one of the systems interacts with the environment, optimization of entanglement and teleportation fidelity requires different strengths of reverse weak measurement. Here, the success probability of optimal protection of entanglement is higher than the success probability of optimal protection of teleportation fidelity. Interestingly, when both systems interact with the environment, optimization of entanglement implies optimization of teleportation fidelity. Therefore, the resources of quantum teleportation along with entanglement need to be explored.
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.
A perfect teleportation protocol requires pure maximally shared entangled states. While in reality the shared entanglement is drastically degraded due to the inevitable interaction with the noisy environment. Here, we propose a teleportation protocol to teleport an unknown qubit through amplitude damping channels with a fidelity up to one with a single copy of the entangled state. Our proposed teleportation protocol, while illustrated using the Bell and W entangled states as examples, can be utilized with any type of entangled states. In our protocol, we utilize environment-assisted measurement (EAM) during the entanglement distribution, and further modify the original teleportation protocol to apply weak measurement in the last step of teleportation. We find a balance between teleportation fidelity and success probability by varying the strength of the weak measurement. Furthermore, we investigate the protection of third-party assisted teleportation protocols, where all the qubits of the entangled state pass through the amplitude damping channel. In particular, for the third-party assisted teleportation with the W state, the decoherence of the shared entanglement can be totally suppressed by using EAM, hence no weak measurement is required to achieve an average teleportation fidelity of unity. The numerical simulation results reveal that our proposed teleportation protocol outperforms both the weak measurement based probabilistic teleportation protocol and the original teleportation protocols without protection.
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 Achieving high‐fidelity quantum teleportation requires the distribution of maximally entangled states through noiseless channels, a condition rarely met in practical implementations. In realistic environments, decoherence processes, such as amplitude damping, severely degrade entanglement quality. In this study, a universal strategy is proposed for protecting entanglement against amplitude damping noise by introducing escort qubits—ancillary qubits specifically designed to assist in the distribution process. This method involves CNOT operations and measurement of the escort qubits. Modeling the amplitude damping channel with a Lindblad master equation, it is showed analytically that the method achieves unit fidelity under ideal operations, independent of the damping rate, with a certain success probability. This method is applied to teleportation with Bell and W states, and compare its performance with weak measurement and environment‐assisted measurement protocols. This approach offers superior fidelity, experimental feasibility, and independence from noise parameters, as confirmed through simulation and Qiskit implementation.
A protective scheme of quantum dense coding and quantum teleportation of the X-type initial state is proposed in amplitude damping noisy channel with memory using weak measurement and measurement reversal. Compared with the noisy channel without memory, the memory factor improves both the capacity of quantum dense coding and the fidelity of the quantum teleportation to a certain extent for the given damping coefficient. Although the memory factor can inhibit decoherence in some degree, it cannot eliminate it completely. In order to further overcome the influence of the damping coefficient, the weak measurement protective scheme is proposed, which found that the capacity and the fidelity can be efficiently improved by adjusting weak measurement parameter. Another practical conclusion is that, among the three initial states, the weak measurement protective scheme has the best protective effect on the Bell-state in terms of the capacity and the fidelity. For the channel with no memory and full memory, the channel capacity of quantum dense coding reaches two and the fidelity of quantum teleportation reaches one for the bit system; the Bell system can recover the initial state completely with a certain probability. It can be seen that the entanglement of the system can be well protected by the weak measurement scheme, which provides a good support for the realization of quantum communication.
We demonstrate a method to preserve entanglement and improve fidelity of three-qubit quantum states undergoing amplitude-damping decoherence using weak measurement and quantum measurement reversal. It is shown that we are able to enhance entanglement to the greatest extent, and to circumvent entanglement sudden death by increasing the weak measurement strength both for the GHZ state and the W state. The weak measurement technique can also enhance the fidelity to the quantum region and even close to 1 for the whole range of the decoherence parameter in both of the two cases. In addition, the W state can maintain more fidelity than the GHZ state in the protection protocol. However, the GHZ state has a higher success probability than the W state.