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Communications in Theoretical Physics

Entanglement and Teleportation of Pair Cat States in Amplitude Decoherence Channel

Xu Hang-Shi, Jing‐Bo Xu

Published Jul 1, 2009• 1 citation
Publisher

Abstract

The dynamic behavior of the entanglement for the pair cat states in the amplitude decoherence channel is studied by adopting the entanglement of formation determined by the concurrence. Then, we consider the teleportation by using joint measurements of the photon-number sum and phase difference with the pair cat states as an entangle resource and discuss the influence of amplitude decoherence on the mean fidelity of the teleportation.

DOI
10.1088/0253-6102/52/1/10

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The dynamic behavior of the entanglement for the pair cat states in the amplitude decoherence channel is studied by adopting the entanglement of formation determined by the concurrence. Then, we consider the teleportation by using joint measurements of the photon-number sum and phase difference with the pair cat states as an entangle resource and discuss the influence of amplitude decoherence on the mean fidelity of the teleportation.
: In this paper, we investigated the entanglement properties of the charge-pair cat states based on the linear entropy function. We used these states for the teleportation of a coherent state in two different measurements at the sender by using joint measurements of the quadrature amplitude and joint measurements of the photon number sum and phase difference. The investigated results of the fidelity show that the even charge-pair cat states are more suitable for teleportation in the way of the quadrature amplitude measurements. However, according to the results of the joint measurement of the photon-number sum and phase difference, both the even and odd charge-pair cat states are suitable for the teleportation process in the small amplitude of the coherent state.
We study an entangled two-mode coherent state within the framework of2×2-dimensional Hilbert space. We investigate the problem of quantum teleportation ofa superposition coherent state via an entangled coherent channel. By three differentmeasures with the titles ``minimum assured fidelity (MASF)”, ``average teleportationfidelity” and ``optimal fidelity (f)” we study the quality of this kind of teleportation.Decoherence properties of the entangled coherent state due to channel losses areanalysed. For a symmetric noise channel, the degradation of optimal fidelity and degreeof entanglement are calculated. Also by two different measures with the titles``concurrence” and ``entanglement of formation” we study the amount of entanglementof a decohered quantum channel and discuss its details. We demonstrate thatentanglement of the decohered entangled coherent state is reduced but not throughlylost. Finally we find that the optimal fidelity of the decohered entangled coherent state ismore than the classical limit and the decohered entangled coherent state may be usefulfor quantum teleportation.
We investigate the entanglement swapping of the continuous variable states by taking the pair Schrödinger cat states as the input entangled states, in which the two-mode squeezed vacuum and the pair cat states serve as the quantum channel, respectively. The entanglement of the initial states as well as the final states is analyzed by adopting the logarithmic negativity as the measure of entanglement. The quantum teleportation task by exploiting the swapped states as the quantum channel is also considered, where a coherent state serves as the target state and the average fidelity is examined.
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.