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IETE Journal of Research

Teleportation of an n -Qubit Superposition State Using Maximally Entangled Greenberger-Horne-Zeilinger (GHZ) Channels

Sujit Chattopadhyay, Debashis Adhikari

Published Dec 3, 2025• 0 citations
Publisher

Abstract

The declaration of 2025 as the International Year of Quantum Science and Technology has galvanized numerous researchers working on innovative quantum applications. Recently, Quantum Computing and Quantum Information Science have gained significant attention as key areas of study within the broader field of Quantum Science and Technology. This is due to their potential to address complex computational challenges, their interdisciplinary applications across diverse fields such as telecommunications and biological sciences, and the intriguing theoretical framework they offer alongside practical implementation challenges. One notable application is Quantum Teleportation (QT), which involves transferring an arbitrary quantum state across spacelike distances using entangled resources. This paper explores the QT of a multi-qubit superposition state, utilizing maximally entangled Greenberger–Horne–Zeilinger (GHZ) states as both the entanglement resource and the basis for quantum measurements. The entire QT procedure is outlined with a notation system that is particularly suited for handling multi-qubit scenarios.

DOI
10.1080/03772063.2025.2588697

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The declaration of 2025 as the International Year of Quantum Science and Technology has galvanized numerous researchers working on innovative quantum applications. Recently, Quantum Computing and Quantum Information Science have gained significant attention as key areas of study within the broader field of Quantum Science and Technology. This is due to their potential to address complex computational challenges, their interdisciplinary applications across diverse fields such as telecommunications and biological sciences, and the intriguing theoretical framework they offer alongside practical implementation challenges. One notable application is Quantum Teleportation (QT), which involves transferring an arbitrary quantum state across spacelike distances using entangled resources. This paper explores the QT of a multi-qubit superposition state, utilizing maximally entangled Greenberger–Horne–Zeilinger (GHZ) states as both the entanglement resource and the basis for quantum measurements. The entire QT procedure is outlined with a notation system that is particularly suited for handling multi-qubit scenarios.
It is well-known that maximally entangled states such as the Greenberger-Horne-Zeilinger (GHZ) states, with the Bell states as the simplest examples, are widely exploited in quantum information and computation. We study the application of such maximally entangled states from the viewpoint of the GHZ transform, which is a unitary basis transformation from the product states to the GHZ states. The algebraic structure of the GHZ transform is made clear and representative examples for it are verified as multi-qubit Clifford gates. In this paper, we focus on the Bell transform as the simplest example of the GHZ transform and apply it to the reformulation of quantum circuit model of teleportation and the reformulation of the fault-tolerant construction of single-qubit gates and two-qubit gates in teleportation-based quantum computation. We clearly show that there exists a natural algebraic structure called the teleportation operator in terms of the Bell transform to catch essential points of quantum teleportation, and hence we expect that there would also exist interesting algebraic structures in terms of the GHZ transform to play important roles in quantum information and computation.
Quantum information processing has a wide range of uses, including the solution of complex algorithms, cryptography, dense coding, quantum computation, and quantum teleportation. Quantum entanglement, a phenomenon that is crucial to many different applications of quantum computation, is an essential resource for quantum computation, and the need for quantum circuits that generate entangled states is one of the ongoing needs for constructing quantum computers. In this study, we present a general approach to the design of quantum circuits that produce entangled states. The approach can be applied to the design of various entanglement circuits with any number of qubits (n-qubit systems), and it makes use of a set of CNOT and Hadamard gates, where the number of CNOT gates should always be (n-1) and each gate connects the two adjacent qubits. In this paper, a three-entangled teleportation scheme of a GHZ-like state (named after its inventor Greenberger-Horne-Zeilinger) through three particles as a quantum channel is presented. The probability of successful teleportation depends on the degree of entanglement of GHZ-like states. A 5-qubit quantum teleportation over a GHZ-like channel has also been used. And single-qubit gates are defined, which are Pauli gates. These gates are represented by arrays I, X, Y, and Z. The results in this paper are good and promising theoretical results in the field of quantum entanglement and quantum teleportation using the Mathematica program.
A scheme for probabilistic controlled teleportation of a triplet W state using combined non-maximally entangled channel of two Einstein–Podolsky–Rosen (EPR) states and one Greenberger–Horne–Zeilinger (GHZ) state is proposed. In this scheme, an (m + 2 )-qubit GHZ state serves not only as the control parameter but also as the quantum channel. The m control qubits are shared by m supervisors. With the aid of local operations and individual measurements, including Bell-state measurement, Von Neumann measurement, and mutual classical communication etc., Bob can faithfully reconstruct the original state by performing relevant unitary transformations. The total probability of successful teleportation is only dependent on channel coefficients of EPR states and GHZ, independent of the number of supervisor m. This protocol can also be extended to probabilistic controlled teleportation of an arbitrary N-qubit state using combined non-maximally entangled channel of N – 1 EPR states and one (m + 2 )-qubit GHZ.
A general scheme for controlled teleportation of an arbitrary multi-qudit state with d -dimensional Greenberger–Horne–Zeilinger (GHZ) states is proposed. For an arbitrary m -qudit state, the sender Alice performs m generalized Bell-state projective measurements on her 2 m qudits and the controllers need only take some single-particle measurements. The receiver Charlie can reconstruct the unknown m -qudit state by performing some single-qudit unitary operations on her particles if she cooperates with all the controllers. As the quantum channel is a sequence of maximally entangled GHZ states, the intrinsic efficiency for qudits in this scheme approaches 100% in principle.
Teleporting an unknown qubit state is a paradigmatic quantum information processing task revealing the advantage of quantum communication protocols over their classical counterpart. For a teleportation protocol using a Bell state as quantum channel, the resource has been identified to be the concurrence. However, for mixed multipartite states the lack of computable entanglement measures has made the identification of the quantum resource responsible for this advantage more challenging. Here, by building on previous results showing that localizable concurrence is the necessary resource for controlled quantum teleportation, we show that any teleportation protocol using an arbitrary multipartite state, that includes a Bell measurement, requires a nonvanishing localizable concurrence between two of its parties to perform better than the classical protocol. By first analyzing Greenberger–Horne–Zeilinger (GHZ) channel and GHZ measurement teleportation protocol, in the presence of GHZ-symmetric-preserving noise, we compare different multipartite entanglement measures with the fidelity of teleportation, and we find that the protocol performs better than the classical protocol when all multipartite entanglement measures vanish, except for the localizable concurrence. Finally, we extend our proof to an arbitrary teleportation protocol with an arbitrary multipartite entangled channel.