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Chinese Physics B

Perfect quantum teleportation and dense coding protocols via the 2N-qubit W state

Mei-Yu Wang, Fengli Yan

Published Dec 1, 2011• 20 citations
Publisher

Abstract

In this paper, we investigate perfect quantum teleportation and dense coding by using an 2 N -qubit W state channel. In the quantum teleportation scheme, an unknown N -qubit entangled state can be perfectly teleported. One ebit of entanglement and two bits of classical communication are consumed in the teleportation process, just like when using the Bell state channel. While N + 1 bits of classical information can be transmitted by only sending N particles in the dense coding protocol.

DOI
10.1088/1674-1056/20/12/120309

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In this paper, we investigate perfect quantum teleportation and dense coding by using an 2 N -qubit W state channel. In the quantum teleportation scheme, an unknown N -qubit entangled state can be perfectly teleported. One ebit of entanglement and two bits of classical communication are consumed in the teleportation process, just like when using the Bell state channel. While N + 1 bits of classical information can be transmitted by only sending N particles in the dense coding protocol.
Quantum mechanics shows superiority than classical mechanics in many aspects and quantum entanglement plays an essential role in information processing and some computational tasks such as quantum teleportation (QT). QT was proposed to transmit the unknown states, in which EPR pairs, the entangled states, can be used as quantum channels. In this paper, we present two simple schemes for teleporting a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state respectively. Alice and Bob have shared an entangle state. Two Bell states are used as quantum channels. Then after Alice measuring her qubits and informing Bob her measurement results, Bob can perfectly reconstruct the original state by performing corresponding unitary operators on his qubits. It shown that a product state of two arbitrary single-particle and an arbitrary two-particle pure entangled state can be teleported perfectly, i.e. the success probabilities of our schemes are both 1.
The beauty of the quantum circuit lies in the fact that it can perform certain tasks which are impossible in the classical world. For example, consider teleportation and superdense coding. Teleportation is a quantum task in which an unknown quantum state is transmitted from a sender (Alice) to a spatially separated receiver (Bob) via an entangled quantum channel and with the help of some classical communications. Dense coding is another communication scheme in which if Alice and Bob share a prior entanglement then one of them can send n bits of classical information to the other by communicating m-qubits (m < n). Before we go into the technical details of these two schemes let us try to lucidly visualize the uniqueness of teleportation. Suppose Alice and Bob are spatially separated and Alice wants to send an unknown quantum state |ψ〉 = α|0〉 + β|1〉 to Bob. For some reason she is not allowed to send the state directly through a quantum channel. She cannot measure it and send the information to Bob because the moment she will try to measure the state, it will collapse either to |0〉 or to |1〉. But the state can be sent by using a simple quantum circuit (pre-shared entanglement) and some classical communications. In the process the unknown quantum state gets destroyed at Alice’s end and reappears at Bob’s end. The state never exists in the communication channel. This process is called quantum teleportation. The uniqueness of quantum teleportation will be clearer if we note that the Fax is not an example of teleportation because the original copy remains with the sender. Again a letter posted in a letter box is not an example of teleportation because the letter exists (travels) in its original form in the communication channel. In brief, there is no classical analogue of quantum teleportation. The same is true for dense coding. In this chapter we will describe these two unique quantum communication schemes and discuss their significance and applications.
We investigate the usefulness of a recently introduced five-qubit state by Brown et al. [I. D. K. Brown, S. Stepney, A. Sudbery, and S. L. Braunstein, J. Phys. A 38, 1119 (2005)] for quantum teleportation, quantum-state sharing, and superdense coding. It is shown that this state can be utilized for perfect teleportation of arbitrary single and two-qubit systems. We devise various schemes for quantum-state sharing of an arbitrary single- and two-particle state via cooperative teleportation. We later show that this state can be used for superdense coding as well. It is found that five classical bits can be sent by sending only three quantum bits.
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$.
Abstract Quantum teleportation and dense coding are quantum tasks in which an unknown quantum state sends from one location to another in first one and a classical bits sends between two locations in the later. We introduce a quantum circuit for creating generalized Bell states discussed by Gustavo Rigolin (PRA 71, 032303 (2005)). We develop appropriate quantum circuit for realizing two qubits teleportation and four bits dense coding. We experimentally demonstrate these circuits in IBM quantum computer and calculate fidelity of teleportation and efficiency of dense coding.