Comment on “Quantum Teleportation via GHZ-Like State”

Abstract

Recently Yang et al. (Int. J. Theor. Phys. 48:516, 2009) have shown that an unknown qubit can be teleported by using a particular GHZ-like state as quantum channel. However, there are several errors in the calculation which lead to incorrect conclusions. The errors have been indicated and corrected. It is also noted that their scheme and the independently proposed teleportation scheme of Zhang et al. (Int. J. Theor. Phys. 48:3331, 2009) uses quantum channel from the same family and any state of that family may be used for teleportation.Keywords Quantum teleportation · GHZ-like state · Fidelity In a recent paper Yang et al. [1] have shown that an unknown qubit can be teleported by using GHZ-like state as quantum channel. In [1] Yang et al. have made some mistakes in calculation. For example, in Sect. 2.1 of [1] they start preparing their channel with a quantum state |φ 1 = |0 1 + |1 1 which is not normalized. Ideally it should read as |φ 1 = 1 √ 2 (|0 1 + |1 1 ). This is important because without this normalization constant the third line of (1) of [1] will not follow from the second line of the same equation. As |φ 1 can be produced by operating Hadamard transformation H on the state |0 , the quantum circuit that prepares the GHZ-like quantum channel used by Yang et al. is essentially two EPR circuits attached in sequence in the cascaded manner (see Fig. 1).After preparing the GHZ-like quantum channel they use that channel to teleport an unknown qubit α|0 + β|1 . To do so, Alice keeps the first two qubits of the channel with

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