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Modern Physics Letters B

OUTPUT AND FIDELITY OF IMPERFECT TELEPORTATION

Yongjian Gu, Chunmei Yao, Zheng-Wei Zhou, Guang‐Can Guo

Published Feb 10, 2004• 0 citations
Publisher

Abstract

Noisy entangled resource and non-standard teleportation operations result in imperfect teleportation. In this paper, we derive an explicit expression for the output states of imperfect teleportation processes, thereby establishing a correspondence between teleportation and quantum channels. This result offers a different insight into teleportation. Also, it enables us to derive an expression for the fidelity of teleportation. Our results analytically reveal the dependence of the output states and the fidelity on the entangled resource and teleportation operations. The Nielsen–Caves teleportation formalism is used in the derivation.

DOI
10.1142/s0217984904006652

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Noisy entangled resource and non-standard teleportation operations result in imperfect teleportation. In this paper, we derive an explicit expression for the output states of imperfect teleportation processes, thereby establishing a correspondence between teleportation and quantum channels. This result offers a different insight into teleportation. Also, it enables us to derive an expression for the fidelity of teleportation. Our results analytically reveal the dependence of the output states and the fidelity on the entangled resource and teleportation operations. The Nielsen–Caves teleportation formalism is used in the derivation.
Teleportation is viewed as a quantum channel. We present an explicit expression for the general teleportation channel in the Kraus decomposition form. We then analyse optimal teleportation procedures for a noisy entangled resource, Bell measurement by the sender and arbitrary operations by the receiver. Our general result allows us to derive the corresponding quantum channel and fidelity, thereby enabling us to formulate the fidelity-based optimization problem and to conclude that this is a problem of semidefinite programming. We offer an alternative viewpoint on optimal teleportation, namely one can perform corrective operations at the receiver's side instead of first manipulating entanglement, and we give an optimal teleportation strategy.
Abstract Causal order can improve the quantum information transmission in teleportation due a noisy entangled resource being present in it by using additionally an appropriate measurement state on the control state ruling the causal order. In this work, we get analytically the fidelity for the entire process under an arbitrary initialization of such control state and performing an optimal measurement on it, thus obtaining a perfect teleportation. We also analyse other values characterizing the imperfect entangled state where a perfect teleportation can not be reached. Notably, we determine that the best fidelity does not depend on the preparation of the control state but instead on the imperfect initial entangled resource.
Quantum teleportation plays an important role in quantum information science. In order to obtain the effect of quantum teleportation of a quantum state by using an entangled resource, the fidelity of teleporting the quantum state should be calculated. Braunstein and Kimble[Phys. Rev. Lett. 80 869 (1998)] derived a formula of calculating the fidelity of quantum teleportation for Gaussian entangled resource and any input state to be teleported. Then, the point is how to calculate the quantum teleportation fidelity for any entangled resource. In this paper, werealize this purpose by using the entangled state representation. First, we derive the Weyl expansion of any density operator by using the completeness relation between coherent state and P-representation. Then using the orthogonal property of entangled state representation and the traditional Kimble-Braunstein scheme of quantum teleportation, we further derive the mean density operator of the output state, which means that we establish the relation between the output density operator and the characteristic functions of the input state to be teleported and the entangled resources. The characteristic function of the output state is also derived which is in the concise form relating these two characteristic functions above. Then we further obtain a new formula for calculating the quantum teleportation fidelity for the coherent state input and any two-mode entangled resource. It is shown that the fidelity of teleportation can be easily calculated when the Q-function of the normally ordering form of entangled resource is known. This is a convenient way of obtaining the fidelity of teleportation. As its applications, some Gaussian and non-Gaussian entangled states are examined to teleport the coherent state, whose results are correct.
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.
Teleportation for pure states, mixed states with standard and optimal protocols are introduced and investigated systematically. An explicit equation governing the teleportation of finite dimensional quantum pure states by a generally given non-local entangled state is presented. For the teleportation of a mixed state with an arbitrary mixed state resource, an explicit expression is obtained for the quantum channel associated with the standard teleportation protocol. The corresponding transmission fidelity is calculated. It is shown that the standard teleportation protocol is not optimal. The optimal quantum teleportation is further studied, its fidelity is given and shown to be related to the fully entangled fraction of the quantum resource, rather than the single fraction as in the standard teleportation protocol.
We study quantum teleportation with the resource of non-orthogonal qubit states. We first extend the standard teleportation protocol to the case of such states. We investigate how the loss of teleportation fidelity resulting from the use of non-orthogonal states compares to a similar loss of fidelity when noisy or non-maximally entangled states are used as the teleportation resource. Our analysis leads to some interesting results on the teleportation efficiency of both pure and mixed non-orthogonal states compared to that of non-maximally entangled and mixed states.