Abstract The purpose of this article is to explore a scheme for controlled double-direction cyclic (DDC) assisted cloning of arbitrary unknown single-qubit states. We first present a construction method for a 13-qubit entangled quantum state using Hadamard gates and controlled-NOT gates, and subsequently generalize it to a ( 4 n + 1 ) -qubit entangled quantum state. Using the 13-qubit entangled state we constructed as a quantum channel, we propose a novel theoretical scheme for achieving five-party controlled DDC-assisted cloning. The first stage of the scheme involves a controlled DDC quantum teleportation, where each of the three communicators can simultaneously teleport two distinct unknown single-qubit states to the other two, under the supervisor’s control. This process ensures that controlled cyclic quantum communication occurs synchronously in both clockwise and anticlockwise directions. In the second stage of the scheme, with the help of special multi-qubit projective measurements from the state preparer, perfect copies or orthogonal complement copies of the two original unknown single-qubit states can be simultaneously created at each sender’s location. Furthermore, the above presented five-party scheme for controlled DDC-assisted cloning can be extended to scenarios with ( n + 1 ) (n > 3) parties by using the ( 4 n + 1 ) -qubit maximally entangled state as the quantum channel. Moreover, we have provided the mathematical expressions for the general analysis of both the sender’s operations and the receiver’s transformations in each scheme. The study shows that the intrinsic efficiency, security, feasibility, and control power of our scheme are good.
Abstract The purpose of this article is to explore a scheme for controlled double-direction cyclic (DDC) assisted cloning of arbitrary unknown single-qubit states. We first present a construction method for a 13-qubit entangled quantum state using Hadamard gates and controlled-NOT gates, and subsequently generalize it to a ( 4 n + 1 ) -qubit entangled quantum state. Using the 13-qubit entangled state we constructed as a quantum channel, we propose a novel theoretical scheme for achieving five-party controlled DDC-assisted cloning. The first stage of the scheme involves a controlled DDC quantum teleportation, where each of the three communicators can simultaneously teleport two distinct unknown single-qubit states to the other two, under the supervisor’s control. This process ensures that controlled cyclic quantum communication occurs synchronously in both clockwise and anticlockwise directions. In the second stage of the scheme, with the help of special multi-qubit projective measurements from the state preparer, perfect copies or orthogonal complement copies of the two original unknown single-qubit states can be simultaneously created at each sender’s location. Furthermore, the above presented five-party scheme for controlled DDC-assisted cloning can be extended to scenarios with ( n + 1 ) (n > 3) parties by using the ( 4 n + 1 ) -qubit maximally entangled state as the quantum channel. Moreover, we have provided the mathematical expressions for the general analysis of both the sender’s operations and the receiver’s transformations in each scheme. The study shows that the intrinsic efficiency, security, feasibility, and control power of our scheme are good.
With the rapid development of quantum communication technologies, controlled double-direction cyclic (CDDC) quantum communication has become an important research direction. However, how to choose an appropriate quantum state as a channel to achieve double-direction cyclic (DDC) quantum communication for multi-particle entangled states remains an unresolved challenge. This study aims to address this issue by constructing a suitable quantum channel and investigating the DDC quantum communication of two-particle states. Initially, we create a 25-particle entangled state using Hadamard and controlled-NOT (CNOT) gates, and provide its corresponding quantum circuit implementation. Based on this entangled state as a quantum channel, we propose two new four-party CDDC schemes, applied to quantum teleportation (QT) and remote state preparation (RSP), respectively. In both schemes, each communicating party can synchronously transmit two different arbitrary two-particle states to the other parties under supervisory control, achieving controlled quantum cyclic communication in both clockwise and counterclockwise directions. Additionally, the presented two schemes of four-party CDDC quantum communication are extended to situations where n>3 communicating parties. In each proposed scheme, we provide universal analytical formulas for the local operations of the sender, supervisor, and receiver, demonstrating that the success probability of each scheme can reach 100%. These schemes only require specific two-particle projective measurements, single-particle von Neumann measurements, and Pauli gate operations, all of which can be implemented with current technologies. We have also evaluated the inherent efficiency, security, and control capabilities of the proposed schemes. In comparison to earlier methods, the results demonstrate that our schemes perform exceptionally well. This study provides a theoretical foundation for bidirectional controlled quantum communication of multi-particle states, aiming to enhance security and capacity while meeting the diverse needs of future network scenarios.
By making use of d-dimensional Hadamard gates and d-dimensional controlled NOT gates, we first construct a five-qudit maximally entangled state, and then use it as the quantum channel to propose a new bidirectional scheme for cloning two different arbitrary unknown single-qudit simultaneously under the assistance from a state preparer and the control of a supervisor. This scheme consists of two stages: quantum teleportation and assisted cloning. To fulfil the purpose, the first stage of this scheme requires bidirectional controlled teleportation via our constructed five-qudit maximally entangled state as quantum channel, where two distant communicators can simultaneously exchange their unknown single-qudit states with unit fidelity and unit probability under the permission of the supervisor.In the second stage,the state preparer disentangles any remaining entangled states by introducing two auxiliary particles, implementing a unitary transformation and two single-particle projective measurements. Subsequently, they transmit a specific number of classical bits to two distinct communicators in order to generate two precise replicas of different unknown states. Subsequently, the above scheme is extended with a certain probability and unit fidelity by replacing the above d-dimensional quantum channel with a five-qudit non-maximally entangled state. Finally, we further analyze the expansion issues of our scheme from the perspectives of positive operator-valued measurement (POVM for short), general quantum channel and the number of state preparers and controllers, and point out that the scheme is secure.
To explore the multi-directional quantum communication in a three-dimensional (3D) system, 13- and [Formula: see text]-qutrit entangled states are constructed by 3D Hadamard gates and 3D controlled NOT gates in this paper. Then we propose a novel theoretical scheme to fulfill four-party double-direction cyclic controlled quantum teleportation (QT) by using a 13-qutrit entangled state as the quantum channel. In this scheme, each observer can teleport two different arbitrary unknown single-qutrit states to the other two observers under the control of the supervisor, respectively and synchronously, which realizes cyclic controlled QT in both clockwise and counterclockwise directions simultaneously. Each observer performs two 3D Bell basis measurements and the supervisor carries out a single-qutrit measurement in the 3D [Formula: see text]-basis. After hearing the measurement results from the other two observers and the supervisor, each observer can restore the target states by utilizing suitable 3D Weyl operators. Based on the [Formula: see text]-qutrit entangled channel that we construct, we exhibit in detail how to extend the presented four-party double-direction cyclic controlled QT scheme to the situation with [Formula: see text] ([Formula: see text]) observers. Analysis shows that the success probability of both the proposed four-party and [Formula: see text]-party schemes can reach 1, and these two schemes are expected to be realized experimentally in the near future. Through detailed discussion, we find that the security of our schemes and the control power of the supervisor can be guaranteed, and the intrinsic efficiency of the proposed schemes is relatively high.
In this paper, two conclusive three-party cyclic assisted cloning protocols in amplitude damping (AD) channel are put forward that, respectively clone three arbitrary unknown single-qubit states and single-qutrit states with the help of a state preparer. Each of our protocols includes three consecutive stages: quantum channel preparation, cyclic quantum teleportation (CQT), and multi-party assisted cloning. The first stage of each protocol proposes the detailed processes of sharing a pure entangled quantum state as a component of a quantum channel in AD channel via entanglement compensation. In second stage, a three-party CQT is presented where three unknown single-qubit states (or single-qutrit states) are reconstructed simultaneously in three different places, respectively, by introducing auxiliary qubits and performing appropriate operations. In the third stage, the state preparer Victor performs one multi-qubit measurement (or one unitary transformation and one multi-qutrit measurement) and informs the three communicators of his outcome, three distinct unknown single-qubit states or their orthogonal complement states (or single-qutrit states) are cloned simultaneously and with probability at three separate locations,respectively. Furthermore, we extend the above protocols from two aspects: (i) the extension to the case of [Formula: see text] participants; (ii) extension to the case of d-dimensional unknown single-qudit state cycle-assisted cloning.
Utilizing Hadamard gates and controlled not gates, maximally entangled states of four, five and six qubits are generated. Then, we propose respectively controlled and assisted cloning schemes of unknown two-, three- and four-qubit states via these constructed states as quantum channels. Each of the three schemes includes two stages: controlled teleportation and assisted cloning. The controlled teleportation stage of our schemes all require a single-qubit [Formula: see text]-basis measurement by controller, and need different GHZ-state measurements by senders of three schemes to complete the transmission process of their respective quantum states. In the assisted cloning stage of our schemes, after the state preparers of three schemes perform respectively appropriate GHZ-state measurements, at the senders’ locations, perfect replicas and orthogonal complementary copies of unknown states will be produced through appropriate local quantum operations. Compared with usual assisted cloning schemes, every suggested plan is extremely efficient in terms of quantum resources, as it only requires a small number of GHZ-state measurements, significantly decreasing the need for quantum operations and classical resources. Through discussion, we conclude that our schemes are safe and can be extended to assisted cloning of unknown multi-qubit GHZ-state with multiple controllers.
In order to explore multi-directional quantum communication in a three-dimensional (3D) system, five-, seven- and [Formula: see text]-qutrit entangled states are constructed by 3D-Hadamard gates and 3D-controlled-NOT gates in this paper. Then a new scheme of controlled bidirectional quantum teleportation (QT) via five-qutrit entangled channel is proposed, where two observers can exchange their unknown single-qutrit states at the same time under the control of the supervisor. Along this mental, we propose a novel theoretical scheme to fulfil four-party controlled cyclic QT by using a seven-qutrit entangled state as the quantum channel, in which Alice can teleport an arbitrary unknown single-qutrit state to Bob, Bob can transmit an arbitrary single-qutrit state to Charlie, at the same time, Charlie can also teleport an arbitrary unknown single-qutrit state to Alice with the permission of the supervisor. In these schemes, only specific two-qutrit 3D-Bell state measurements, single-qutrit 3D-Z-basis measurements and suitable 3D-Weyl operators are needed, which can be implemented in physics easily. Moreover, the proposed four-party controlled cyclic scheme can be generalized into the case containing [Formula: see text] ([Formula: see text]) observers by using a [Formula: see text]-qutrit entangled channel. Analysis shows that the success probability of our schemes can reach 1. Through detailed discussion, we find that the security of our schemes and the control power of the supervisors can be guaranteed, and the intrinsic efficiency of the proposed schemes is relatively high.