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Communications in Theoretical Physics

Average Fidelity of Teleportation in Quantum Noise Channel

Hao Xiang, Rong Zhang, Zhu Shi-Qun

Published May 1, 2006• 7 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/45/5/008

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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.
We investigate the influence of amplitude damping at every stage of the unitary operation of controlled teleportation of a qubit by a tripartite W state in the Bloch sphere representation. We use the average fidelity to describe how much information is transferred from the initial state to the teleported state. It is shown that when a depolarized three-particle W state is used as the quantum channel, the average fidelity of teleportation is a function of the decoherence rate p and the depolarizing rate p '. The larger the depolarizing rate is, the smaller the amplitude damping effect on the average fidelity is. Moreover, the average fidelity of teleportation with values larger than 2/3 can be obtained when the values of p and p ' are chosen properly.
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.
A new analytical expression for the average quantum fidelity of a teleportation protocol for an arbitrary two-qubit state transmitted through an amplitude-damping noise environment has been established. This expression shows that the average fidelity depends not only on the purity measure and the bipartite entanglement measure of each parallel state forming the quantum channel, but also on the multipartite entanglement measure. This entanglement is generated between the qubits of each parallel state when they interact independently with the amplitude-damping environment. Based on this analytical relation, the physical mechanism for enhancing the teleportation protocol’s average quantum fidelity under two distinct amplitude-damping noise scenarios has been elucidated.
We consider the problem of teleporting superposed coherent state using non-maximally entangled coherent state as quantum channel and study the effect of entanglement over quality of teleportation. We show that if maximally entangled coherent state (MECS) used by Van Enk and Hirota [Phys. Rev. A 64, 022313 (2001)] and by H Prakash et al. [Phys. Rev. A 75, 044305 (2007)] is replaced by a particular non-maximally entangled coherent state (NMECS), average fidelity of quantum teleportation increases appreciably at small coherent amplitudes. Since it is very challenging to produce superposed coherent states of large coherent amplitudes, the particular NMECS appear to be a good quantum channel for teleportation at small coherent amplitudes for practical implementation.
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.
Abstract Quantum teleportation, a cornerstone of quantum information processing, faces critical challenges from environmental noise such as amplitude damping (AD), which degrades entanglement and reduces teleportation fidelity below the classical limit of 2/3. This study investigates the role of parity-time ( PT ) symmetric operations, a type of non-Hermitian operation, in enhancing teleportation fidelity under AD noise. We first derive the explicit dynamics of entangled states subjected to AD noise using Kraus operators, showing that the average fidelity decays monotonically with increasing decoherence strength. By introducing local PT symmetric operations, we show the average fidelity exhibits periodic linear oscillations, with minimum values increasing with non-Hermiticity and remaining above 2/3, while maximum fidelity consistently reaches the optimal value of 1. These results confirm that non-Hermitian operations effectively protect quantum teleportation fidelity, maintaining stability and optimal performance despite parameter variations. Experimental feasibility is discussed using nuclear magnetic resonance systems with duality quantum computing techniques.