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<p>This comment re-examines the scheme proposed by Kazemikhah et al. [Int. J. Theor. Phys. 60, 378–386 (2021)] for bidirectional quantum teleportation of arbitrary <i>n</i>-qubit states using a four-qubit cluster state. Our analysis reveals that the protocol does not fully realize the intended <i>n</i>-qubit bidirectional teleportation. Specifically, the state-reduction and state-reconstruction procedures operate correctly only for particular two-, three-, or four-qubit states of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\alpha _0| 00.. \rangle + \alpha _1| 11.. \rangle )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>α</mi> <mn>0</mn> </msub> <mo stretchy="false">|</mo> <mn>00</mn> <mo>.</mo> <mo>.</mo> <mo stretchy="false">⟩</mo> </mrow> <mo>+</mo> <msub> <mi>α</mi> <mn>1</mn> </msub> <mrow> <mo stretchy="false">|</mo> <mn>11</mn> <mo>.</mo> <mo>.</mo> <mo stretchy="false">⟩</mo> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Therefore, the protocol can bidirectionally teleport only such specific states rather than an arbitrary <i>n</i>-qubit state. Additionally, we also show that the entangled channel employed in the protocol does not correspond to a true four-qubit cluster state. Nonetheless, the work of Kazemikhah et al. provides an important conceptual foundation for reduction–reconstruction strategies, which has subsequently motivated related research, including the <i>N</i>-qubit GHZ-like state teleportation scheme proposed in 10.1063/5.0179501.</p>

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Comment on "Bidirectional Quantum Teleportation of an Arbitrary Number of Qubits by Using Four Qubit Cluster State"

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Muhammad Taufiqi,
  • Agus Purwanto

摘要

This comment re-examines the scheme proposed by Kazemikhah et al. [Int. J. Theor. Phys. 60, 378–386 (2021)] for bidirectional quantum teleportation of arbitrary n-qubit states using a four-qubit cluster state. Our analysis reveals that the protocol does not fully realize the intended n-qubit bidirectional teleportation. Specifically, the state-reduction and state-reconstruction procedures operate correctly only for particular two-, three-, or four-qubit states of the form \((\alpha _0| 00.. \rangle + \alpha _1| 11.. \rangle )\) ( α 0 | 00 . . ⟩ + α 1 | 11 . . ⟩ ) . Therefore, the protocol can bidirectionally teleport only such specific states rather than an arbitrary n-qubit state. Additionally, we also show that the entangled channel employed in the protocol does not correspond to a true four-qubit cluster state. Nonetheless, the work of Kazemikhah et al. provides an important conceptual foundation for reduction–reconstruction strategies, which has subsequently motivated related research, including the N-qubit GHZ-like state teleportation scheme proposed in 10.1063/5.0179501.