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arXiv:0905.4362 · International Journal of Quantum Information

TELEPORTING BIPARTITE ENTANGLEMENT USING MAXIMALLY ENTANGLED MIXED CHANNELS

Steve Campbell, Mauro Paternostro

Published Feb 1, 2010• 4 citations
arXivHTMLPDF

Abstract

The ability to teleport entanglement through maximally entangled mixed states as defined by concurrence and linear entropy is studied. We show how the teleported entanglement depends on the quality of the quantum channel used, as defined through its entanglement and mixedness, as well as the form of the target state to be teleported. We present new results based on the fidelity of the teleported state as well as an experimental setup that is immediately implementable with currently available technology.

DOI
10.1142/s021974991000606x

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The ability to teleport entanglement through maximally entangled mixed states as defined by concurrence and linear entropy is studied. We show how the teleported entanglement depends on the quality of the quantum channel used, as defined through its entanglement and mixedness, as well as the form of the target state to be teleported. We present new results based on the fidelity of the teleported state as well as an experimental setup that is immediately implementable with currently available technology.
We present a mathematical formulation of old teleportation protocol (original teleportation protocol introduced by Bennett et al.) for mixed state and study in detail the role of mixedness of the two-qubit quantum channel in a teleportation protocol. We show that maximally entangled mixed state described by the density matrix of rank-4 will be useful as a two-qubit teleportation channel to teleport a single qubit mixed state when the teleportation channel parameter p1 > 1/2. Also we discuss the case when p1 ≤ 1/2.
We study the efficiency of two-qubit mixed entangled states as resources for quantum teleportation. We first consider two maximally entangled mixed states, viz., the Werner state\cite{werner}, and a class of states introduced by Munro {\it et al.} \cite{munro}. We show that the Werner state when used as teleportation channel, gives rise to better average teleportation fidelity compared to the latter class of states for any finite value of mixedness. We then introduce a non-maximally entangled mixed state obtained as a convex combination of a two-qubit entangled mixed state and a two-qubit separable mixed state. It is shown that such a teleportation channel can outperform another non-maximally entangled channel, viz., the Werner derivative for a certain range of mixedness. Further, there exists a range of parameter values where the former state satisfies a Bell-CHSH type inequality and still performs better as a teleportation channel compared to the Werner derivative even though the latter violates the inequality.
In this paper, we propose a protocol to deterministically teleport an unknown mixed state of qubit by utilizing a maximally bipartite entangled state of qubits as quantum channel. If a non-maximally entangled bipartite pure state is employed as quantum channel, the unknown mixed quantum state of qubit can be teleported with 1−(1− C 2 ) 1/2 probability, where C is the concurrence of the quantum channel. The protocol can also be generalized to teleport a mixed state of qudit or a multipartite mixed state. More important purpose is that, on the basis of the protocol, the teleportation of an arbitrary multipartite (pure or mixed) quantum state can be decomposed into the teleportation of each subsystem by employing separate entangled states as quantum channels. In the case of deterministic teleportation, Bob only needs to perform unitary transformations on his single particles in order to recover the initial teleported multipartite quantum state.
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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.
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.