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Communications in Theoretical Physics

Standard Teleportation of One-Qubit State and Partial Teleportation of Two-Qubit State via X-States

Meng Qin, Xu Sheng-Long, Xiao-Yue Zhai

Published Feb 1, 2012• 7 citations
Publisher

Abstract

In this article, we derive the explicit entanglement and fidelity expressions for a larger class of two-qubit states, namely, a seven-parameter family of so called X-states. The analytical expressions of the entanglement, the output entanglement and the average fidelity are obtained for this general model by using the concept of concurrence and average fidelity. We study the relations between quantum entanglement, the output entanglement, and the average fidelity for standard teleportation of one-qubit and partial teleportation of two-qubit state. We discover that the average fidelity and entanglement is not a simple dependence relation. The higher entangled system is helpful for teleportation.

DOI
10.1088/0253-6102/57/2/06

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In this article, we derive the explicit entanglement and fidelity expressions for a larger class of two-qubit states, namely, a seven-parameter family of so called X-states. The analytical expressions of the entanglement, the output entanglement and the average fidelity are obtained for this general model by using the concept of concurrence and average fidelity. We study the relations between quantum entanglement, the output entanglement, and the average fidelity for standard teleportation of one-qubit and partial teleportation of two-qubit state. We discover that the average fidelity and entanglement is not a simple dependence relation. The higher entangled system is helpful for teleportation.
Quantum entanglement and teleportation of two qubit X-states subject to heat bath is investigated by partial teleportation protocol. We obtain the analytical expressions of the average fidelity for the X-states with one-side decoherence and two-side decoherence. The quality of quantum teleportation with various initial states is investigated by explicitly calculating the concurrence, the output concurrence and the average fidelity. The results demonstrate that the model is suitable for teleportation, which depends on the initial state. However, the mean thermal occupation number of bath and decoherence could induce the decrease of the output entanglement and the average fidelity in the quantum teleportation processing. We also find the quantum teleportation protocol of one-side decoherence is more robust than that of under two-side decoherence.
We analyze quantum teleportation for composite systems, specifically for concatenated teleporation (decomposing a large composite state into smaller states of dimension commensurate with the channel) and partial teleportation (teleporting one component of a larger quantum state). We obtain an exact expression for teleportation fidelity that depends solely on the dimension and singlet fraction for the entanglement channel and entanglement (measures by III concurrence) for the state; in fact quantum teleportation for composite systems provides an operational interpretation for III concurrence. In addition we obtain tight bounds on teleportation fidelity and prove that the average fidelity approaches the lower bound of teleportation fidelity in the high-dimension limit.
Abstract Quantum teleportation with an arbitrary two-qubit state can be appropriately characterized in terms of maximal fidelity and fidelity deviation. The former quantifies optimality of the process and is defined as the maximal average fidelity achievable within the standard protocol and local unitary strategies, whereas the latter, defined as the standard deviation of fidelity over all input states, is a measure of fidelity fluctuations. The maximal fidelity for a two-qubit state is known and is given by a simple formula that can be exactly computed, but no such formula is known for the fidelity deviation. In this paper, we derive an exact computable formula for the fidelity deviation in optimal quantum teleportation with an arbitrary state of two qubits. From this formula, we obtain the dispersion-free condition, also known as the universality condition: the condition that all input states are teleported equally well and provide a necessary and sufficient condition for a state to be both useful (maximal fidelity larger than the classical bound) and universal (zero fidelity deviation). We also show that for any given maximal fidelity, larger than the classical bound, there always exist dispersion-free or universal states and argue that such states are the most desirable ones within the set of useful states. We illustrate these results with well-known families of two-qubit states: pure entangled states, Bell-diagonal states, and subsets of X states.
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.
In this article, we find a theorem that gives a relation between the maximal fidelity of teleportation and the concurrence of the inseparable XXX state used as a quantum channel in this process. Furthermore, we evaluate the concurrence of the output states generated by the local and nonlocal asymmetric broadcasting of entanglement and prove that the concurrence is greater in the case of nonlocal broadcasting. We analyze the possibility of using the output states obtained by the broadcasting of entanglement as quantum channels in quantum teleportation. We prove, with the help of the above-mentioned theorem, that all the inseparable states given by the local and nonlocal asymmetric broadcasting of entanglement are useful for quantum teleportation. Finally, we show that the maximal fidelity of teleportation is greater in the case when the second scenario is used, i.e., when the quantum channel is generated by the nonlocal asymmetric broadcasting of entanglement.