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arXiv:2107.12169 · Modern Physics Letters A

Two-way ↔ quantum communication using four-qubit cluster state: Mutual exchange of quantum information

Vikram Verma, Mitali Sisodia

Published Feb 10, 2022• 7 citations

Abstract

In this study, we have proposed a scheme for two-way quantum communication in which the two legitimate participants mutually exchange their quantum information to each other by using a four-qubit cluster state as the quantum channel. Recently, by utilizing four-qubit cluster state as the quantum channel, Kazemikhah et al. [Int. J. Theor. Phys. 60, 378 (2021)] tried to design a scheme for mutual exchange of quantum information between two legitimate participants. However, in this study, it has been shown that in their scheme, the transmission of quantum information cannot be realized because the two participants are not entangled to each other due to a trivial conceptual mistake made by Kazemikhah et al. in the description of the quantum channel. Here, we have shown that two legitimate participants can teleport quantum information states to each other by using four-qubit cluster state as the quantum channel, provided they co-operate with each other and perform nonlocal controlled phase gate operation. If both participants do not co-operate with each other, then no one can reconstruct the information sent to them, and therefore, the exchange of information is possible only when both participants are honest to each other.

DOI: 10.1142/s0217732322500201

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In this study, we have proposed a scheme for two-way quantum communication in which the two legitimate participants mutually exchange their quantum information to each other by using a four-qubit cluster state as the quantum channel. Recently, by utilizing four-qubit cluster state as the quantum channel, Kazemikhah et al. [Int. J. Theor. Phys. 60, 378 (2021)] tried to design a scheme for mutual exchange of quantum information between two legitimate participants. However, in this study, it has been shown that in their scheme, the transmission of quantum information cannot be realized because the two participants are not entangled to each other due to a trivial conceptual mistake made by Kazemikhah et al. in the description of the quantum channel. Here, we have shown that two legitimate participants can teleport quantum information states to each other by using four-qubit cluster state as the quantum channel, provided they co-operate with each other and perform nonlocal controlled phase gate operation. If both participants do not co-operate with each other, then no one can reconstruct the information sent to them, and therefore, the exchange of information is possible only when both participants are honest to each other.

Abstract By utilizing the four-qubit cluster state as quantum channel, two efficient quantum schemes for teleporting an arbitrary single-qubit state in a controlled manner are put forward. In one scheme the controller needs to dominate a qubit only, while in another scheme the controller has to hold two qubits. The inspection of the necessary operations indicates that both schemes are feasible in terms of the current technologies. Moreover, these two schemes are compared with two competing schemes which employ the same quantum channel [i.e., the JM-schemes proposed by Jiang and Mo, Int. J. Theor. Phys. 56, 3084 (2017)]. It is found that, in contrast to the JM-schemes, the schemes we proposed have some prominent advantages, such as lower consumption of classical information, fewer necessary local quantum operations, and higher intrinsic efficiency.

Abstract Based on the four-qubit cluster state as quantum channel, we put forward a novel scheme for teleporting a two-qubit arbitrary entangled state. The necessary quantum operations for accomplishing the task are two controlled-not gate operations, one controlled-phase gate operation, four single-qubit measurements and two single-qubit transformed operations. They are easily achievable with current experimental techniques. Besides, the present scheme is deterministic because its probability of success is 100 % .

In order to complete the quantum teleportation,we propose a quantum teleportation scheme of arbitrary twoqubit cluster state by using a four-qubit cluster state based on quantum entanglementphenomenon in this paper. In this scheme,the sender and the receiver share a four-qubit cluster state. The sender first performs a joint von-Neumann measurement on the qubits in his hand. And he sends the measurement results to the receiver through the classical channel. The receiver performs corresponding unitary operation according to the measurement results he received. In the process of this communication,the sender does not tell the original arbitrary two-qubit cluster state to the receiver,but he reconstructs the arbitrary two-qubit state. The quantum teleportation comes true through these processes and the mutual communication is completed.

A scheme of using four-qubit cluster state as quantum channel(QC)to convey the quantum state information is proposed to realize two-way communication.In this scenario,two sides of communication,Alice and Bob,share a four-qubit cluster state.In the process of communication,at first,four-qubit cluster state form a whole system with quantum state information two sides have.Then,Alice and Bob perform Bell-state joint measurements to their own part qubits respectively,and tell the measured results to each other via classical channel(CC).Finally,according to the measured results,Alice and Bob make corresponding unitary transformations,hence its own party can reappear the opposite quantum state information.So two-way communication of quantum state information is achieced.

Utilizing a six-qubit cluster state as quantum channel, a bidirectional controlled quantum teleportation (BCQT) scheme was put forward by Yan in [Int. J. Theor. Phys. 52, 3870 (2013)]. However, in order to accomplish the task, two agents must cooperate to perform a quantum controlled phase gate operation on their two qubits. In view of the present technique, such kind of remote joint operation is difficult to be realized. In this paper, based on the same cluster state, we propose a different BCQT scheme to avoid the remote joint operation. Besides, an unnecessary waste of classical messages in Yan’s scheme is point out.

Quantum teleportation provides a “bodiless” way of transmitting the quantum state from one object to another, at a distant location, using a classical communication channel and a previously shared entangled state. In this paper, we present a tripartite scheme for probabilistic teleportation of an arbitrary single qubit state, without losing the information of the state being teleported, via a fourqubit cluster state of the form | ϕ > 1234 = α |0000>+ β |1010>+ γ |0101>- η |1111>, as the quantum channel, where the nonzero real numbers α , β , γ , and η satisfy the relation j α j2 + | β | 2 + | γ | 2 + | η | 2 = 1. With the introduction of an auxiliary qubit with state |0>, using a suitable unitary transformation and a positive-operator valued measure (POVM), the receiver can recreate the state of the original qubit. An important advantage of the teleportation scheme demonstrated here is that, if the teleportation fails, it can be repeated without teleporting copies of the unknown quantum state, if the concerned parties share another pair of entangled qubit. We also present a protocol for quantum information splitting of an arbitrary two-particle system via the aforementioned cluster state and a Bell-state as the quantum channel. Problems related to security attacks were examined for both the cases and it was found that this protocol is secure. This protocol is highly efficient and easy to implement.