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arXiv:quant-ph/0206173 · Physical Review A

Fidelity of quantum teleportation through noisy channels

Sangchul Oh, Soonchil Lee, Hai-Woong Lee

Published Aug 27, 2002• 200 citations
arXivHTMLPDF

Abstract

We investigate quantum teleportation through noisy quantum channels by solving analytically and numerically a master equation in the Lindblad form. We calculate the fidelity as a function of decoherence rates and angles of a state to be teleported. It is found that the average fidelity and the range of states to be accurately teleported depend on types of noises acting on quantum channels. If the quantum channels are subject to isotropic noise, the average fidelity decays to $1/2,$ which is smaller than the best possible value of $2/3$ obtained only by the classical communication. On the other hand, if the noisy quantum channel is modeled by a single Lindblad operator, the average fidelity is always greater than $2/3.$

DOI
10.1103/physreva.66.022316

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We investigate quantum teleportation through noisy quantum channels by solving analytically and numerically a master equation in the Lindblad form. We calculate the fidelity as a function of decoherence rates and angles of a state to be teleported. It is found that the average fidelity and the range of states to be accurately teleported depend on types of noises acting on quantum channels. If the quantum channels are subject to isotropic noise, the average fidelity decays to 1/2,1/2,1/2, which is smaller than the best possible value of 2/32/32/3 obtained only by the classical communication. On the other hand, if the noisy quantum channel is modeled by a single Lindblad operator, the average fidelity is always greater than 2/3.2/3.2/3.
Quantum teleportation plays a significant role in the field of quantum communication. This paper investigates quantum teleportation through a noisy environment by using GHZ state and non-standard W state as quantum channels. We analyze the efficiency of quantum teleportation by solving analytically a master equation in Lindblad form. Following the quantum teleportation protocol, we obtain the fidelity of quantum teleportation as a function of evolution time. The calculation results show that the teleportation fidelity using non-standard W is higher in comparison to GHZ state at the same evolution time. Moreover, we consider the efficiency of teleportation with weak measurements and reverse quantum measurement under amplitude damping noise. Our analysis suggests that the teleportation fidelity using non-standard W is also more robust to noise than GHZ state in the same conditions. Interestingly, we found that weak measurement and its reverse operation have no positive effect on the efficiency of quantum teleportation by using GHZ and non-standard W state in the amplitude damping noise environment. In addition, we also demonstrate the efficiency of quantum teleportation can be improved by making minor modifications to the protocol.
In this work, we investigate controlled quantum teleportation in the presence of noisy channels acting on the three-qubit resource state. We employ a series of generalized noisy channels that bridge the dephasing channels and amplitude damping channels while encompassing extensive intermediate scenarios. We provide an in-depth analysis of the degradation of the maximal average fidelity and the optimal average fidelity in controlled quantum teleportation induced by such noisy channels by deriving the analytical expression and examining several special cases. The analytical expression shows that attaining the optimal average fidelity requires Charlie's cooperation in performing a measurement at suitably chosen angles, and is also related to the initial state and the channel parameters. Our analysis reveals that the optimal average fidelity does not always decrease monotonically with the evolution parameter, instead, it first decreases and then increases. This non-monotonic behavior depends on the entanglement of the initial resource state, as well as on the parameters of the channel traversed by the first qubit.
We study standard quantum teleportation of a one-qubit state for the situation in which the channel is subject to decoherence, and where the evolution of the channel state is ruled by a master equation in the Lindblad form. A detailed calculation reveals that the quality of teleportation is determined by both the entanglement and the purity of the channel state, and only the optimal matching of them ensures the highest fidelity of standard quantum teleportation. Also our results demonstrated that the decoherence induces distortion of the Bloch sphere for the output state with different rates in different directions, which implies that different input states will be teleported with different fidelities.
In quantum information theory, effects of quantum noise on teleportation are undeniable. Hence,we investigate the effect of noisy channels including amplitude damping, phase damping, depolarizing and phase ip on the teleported state between Alice and Bob where they share an entangled state by using atom-eld interaction state. We analyze the delity and quantum correlations as a function of decoherence rates and time scale of a state to be teleported. We observe that the average delityand quantum correlations accurately depend on types of noise acting on quantum channels. It is found that atom-eld interaction states are affected by amplitude damping channel are more useful for teleportation than when the shared qubites are affected by noisy channels such as AD channel and phase ip. We also observe that if the quantum channels is subject to phase ip noise, the average delity reproduces initial quantum correlations to possible values. On the other hand,not only all the noisy quantum channels do not always destroy average delity but also they can yield the highest delity in noisy conditions. In the current demonstration, our results provide that the average delity can have larger than 2/3 in front of the noise of named other channels with increasing decoherenc strength. Success in quantum states transfer in the present noise establishes the important of studing noisy channels.
The effects of amplitude damping in quantum noise channels on average fidelity of quantum teleportation are analyzed in Bloch sphere representation for every stage of teleportation. When the quantum channels are varied from maximally entangled states to non-maximally entangled states, it is found that the effects of noise channels on the fidelity are nearly equivalent to each other for strong quantum noise. The degree of damage on the fidelity of non-maximally entangled channels is smaller than that of maximally entangled channels. The average fidelity of values larger than 2/3 may be one representation indirectly showing how much the unavoidable quantum noise is.
Quantum teleportation channels can overcome the effects of photonic loss, a major challenge in the implementation of a quantum network over fiber. Teleportation channels are created by distributing an entangled state between two nodes, which is a probabilistic process requiring classical communication. This causes critical delays that can cause information loss as quantum data suffers from decoherence when stored in memory. In this work, we quantify the effect of decoherence on fidelity at a node in a quantum network due to the storage of qubits in noisy memory platforms. We model a memory platform as a buffer that stores incoming qubits waiting for the creation of a teleportation channel. Memory platforms are parameterized with decoherence rate and buffer size. We show that fidelity at a node is a linear sum of terms, exponentially decaying with time, where the decay rate depends on the decoherence rate of the memory platform. This allows us to utilize Laplace transforms to derive computable functions of average fidelity with respect to the load, buffer size, and decoherence rate of the memory platform. We prove that serving qubits in a Last In First Out order with pushout for buffer overflow management maximizes average fidelity. Last, we apply this framework to model a single repeater node to calculate the average fidelity of the end-to-end entanglement created by this repeater assuming perfect gate operations.