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arXiv:0705.1917

Teleportation and Superdense coding with Genuine quadripartite entangled states

Pradhan, B., Pankaj Agrawal, Arun Kumar Pati

Published May 14, 2007• 7 citations
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Abstract

We investigate the usefulness of different classes of genuine quadripartite entangled states as quantum resources for teleportation and superdense coding. We examine the possibility of teleporting unknown one, two and three qubit states. We show that one can use the teleportation protocol to send any general one and two qubit states. A restricted class of three qubit states can also be faithfully teleported. We also explore superdense coding protocol in single-receiver and multi-receiver scenarios. We show that there exist genuine quadripartite entangled states that can be used to transmit four cbits by sending two qubits. We also discuss some interesting features of multi-receiver scenario under LOCC paradigm.

DOI
10.48550/arxiv.0705.1917

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As we know, the states of triqubit systems have two important classes: GHZ-class and W-class. In this paper, the states of W-class are considered for teleportation and superdense coding, and they are generalized to multi-particle systems. First we describe two transformations on the shared resources for teleportation and superdense coding. With these transformations, we obtain a sufficient and necessary condition for a state of W-class being suitable for perfect teleportation and superdense coding. For the state which was thought to be not suitable for sending three classical bits by sending two qubits by Agrawal and Pati (2006 Phys. Rev. A 74 062320), we show that it may be used to fulfil that task, if entangled unitary operations on two qubits are allowed. We generalize the states of W-class to multi-qubit systems and multi-particle systems with higher dimension. We propose two protocols for teleportation and superdense coding by using W-states of multi-qubit systems that generalize the protocols by using | W ⟩ 123 proposed by Agrawal and Pati. We obtain an optimal way to partition some W-states of multi-qubit systems into two subsystems, such that the entanglement between them achieves maximum value.
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We consider W-states and generalized W-states for nnn-qubit systems. We obtain conditions to use these states as quantum resources to teleport unknown states. Only a limited class of multi-qubit states can be teleported. For oneoneone-qubit states, we use protocols which are simple extensions of the conventional teleportation protocol. We also show that these resource states can be used to transmit {\em at most} n+1n + 1n+1 classical bits by sending nnn qubits if the appropriate conditions are met. Therefore these states are not suitable for maximal teleportation or superdense coding when $ n > 3$.