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Communications in Theoretical Physics

Effects of Phase Damping on Controlled Teleportation of a Qubit by a GHZ State

Xiao-Ping Han, Liu Jin-Ming

Published Apr 1, 2008• 5 citations
Publisher

Abstract

We investigate controlled teleportation of a qubit via a GHZ state with the influence of phase damping in the Bloch sphere representation. We use the average trace distance to describe how close the output state is to the input state to be teleported. Our results show that the average trace distance is a function of decoherence rates and angles of the analyzer performed by the controller in the single-particle projective measurement. Moreover, for a fixed value of the decoherence rate, one can adjust the analyzer angle to achieve the optimal average trace distance.

DOI
10.1088/0253-6102/49/4/19

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We investigate controlled teleportation of a qubit via a GHZ state with the influence of phase damping in the Bloch sphere representation. We use the average trace distance to describe how close the output state is to the input state to be teleported. Our results show that the average trace distance is a function of decoherence rates and angles of the analyzer performed by the controller in the single-particle projective measurement. Moreover, for a fixed value of the decoherence rate, one can adjust the analyzer angle to achieve the optimal average trace distance.
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.
The entanglement behavior of two classes of multi-qubit system, GHZ and GHZ like states passing through a generalized amplitude damping channel is discussed. Despite this channel causes degradation of the entangled properties and consequently their abilities to perform quantum teleportation, one can always improve the lower values of the entanglement and the fidelity of the teleportrd state by controlling on Bell measurements, analyzer angle and channel's strength. Using GHZ-like state within a generalized amplitude damping channel is much better than using the normal GHZ-state, where the decay rate of entanglement and the fidelity of the teleported states are smaller than those depicted for GHZ state.
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.
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.
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.