Abstract We concern on the cyclic controlled remote preparation of qudit states in a chain network. By choosing proper entanglement resources, we first propose a unidirectional scheme where single-qudit states can be deterministically prepared clockwise among multiple users. Each sender executes a positive operator-value measure under the elaborately constructed basis and a projective measurement (PM) under the generalized X basis, while the controller carries out a PM under the generalized Z basis. The corresponding receiver can restore the target state by executing recovery operations which is deduced by universal formulas. Then, we present a bidirectional scheme such that each sender can prepare two single-qudit states in both clockwise and counterclockwise directions. It is worth stressing that network coding is applied at the controller’s site to reduce the classical communication cost. The schemes are further extended to arbitrary multi-particle systems. Additionally, we consider the impact of amplitude damping noise and phase damping noise, and employ the strategy of weak measurement to counteract noise.
Abstract We concern on the cyclic controlled remote preparation of qudit states in a chain network. By choosing proper entanglement resources, we first propose a unidirectional scheme where single-qudit states can be deterministically prepared clockwise among multiple users. Each sender executes a positive operator-value measure under the elaborately constructed basis and a projective measurement (PM) under the generalized X basis, while the controller carries out a PM under the generalized Z basis. The corresponding receiver can restore the target state by executing recovery operations which is deduced by universal formulas. Then, we present a bidirectional scheme such that each sender can prepare two single-qudit states in both clockwise and counterclockwise directions. It is worth stressing that network coding is applied at the controller’s site to reduce the classical communication cost. The schemes are further extended to arbitrary multi-particle systems. Additionally, we consider the impact of amplitude damping noise and phase damping noise, and employ the strategy of weak measurement to counteract noise.
Abstract By elaborately selecting entangled channel, we put forward a universal scheme to achieve bidirectional remote preparation of qudit states with arbitrary numbers of particles under the control of the supervisor. Each sender needs to perform a positive-operator-value measurement and a projective measurement, while the supervisor requires to execute a projective measurement. Based on their measurement outcomes, the receivers can recover the desired states concurrently by carrying out single-qudit generalized Pauli operations which are given by general formulas. A point to highlight is that classical communication cost is greatly reduced at the supervisor’s broadcast channel by taking advantage of network coding. In addition, we analyze the influence of amplitude-damping and phase-damping noises, and utilize weak measurement and environment-assisted measurement to suppress noise.
Abstract Our concern is to investigate controlled remote implementation of partially unknown operations with multiple layers. We first propose a scheme to realize the remote implementation of single-qubit operations belonging to the restricted sets. Then, the proposed scheme is extended to the case of single-qudit operations. As long as the controller and the higher-layer senders consent, the receiver can restore the desired state remotely operated by the sender. It is worth mentioning that the recovery operation is deduced by general formulas which clearly reveal the relationship with the measurement outcomes. For the sake of clarity, two specific examples with two levels are given respectively. In addition, we discuss the influence of amplitude-damping noise and utilize weak measurement and measurement reversal to effectively resist noise.
Abstract Based on the demand for safer and more efficient quantum network communication, we propose two deterministic protocols to achieve the remote preparation of an arbitrary n-qudit equatorial states among multiple agents by selecting appropriate entanglement resources. The level of the agents varies depending on their authorities to restore the secret state. The superior agent requires the cooperation of the residual superior agents and any one of the subordinate agents, while the subordinate agent needs the help of all the other agents. To be emphasized, the recovery operations are deduced by general formulas that distinctly elucidate their relevance with the measurement outcomes. Additionally, we discuss the impact of amplitude damping noise and utilize weak measurement and measurement reversal to suppress noise.
Abstract Multi-party quantum communication has gradually attracted widespread attention. To realize the perfect transmission of quantum states among multiple participants, a novel multi-party controlled cyclic remote preparation protocol for arbitrary single-qubit states with three senders is proposed. With the permission of one controller, each sender can transmit an arbitrary single-qubit state to its neighbor. In addition, we give a universal protocol for multi-party controlled cyclic remote preparation of arbitrary single-qubit states in the case of multiple senders, which can realize deterministic cyclic preparation of multiple quantum states in one direction. The scheme shows that the communication task can be successfully achieved only if all senders cooperate with the controller, and there is no need for the senders to employ information splitting and additional operations before performing measurements. Finally, we discuss the cyclic remote preparation protocol with three senders under five types of noisy environment, and the closeness between the output state and original state is measured by calculating fidelity.
We propose two multi-layer controlled multi-output remote state preparation (RSP) schemes for arbitrary single-qubit and single-qudit states. Twelve-particle entangled channels are constructed in two-dimensional and d-dimensional Hilbert spaces, and a hierarchical authorization mechanism is introduced to enable controllers with different permission levels to jointly and selectively regulate the reconstruction of quantum states at multiple receivers. First, based on a twelve-qubit maximally entangled channel, we design a deterministic three-layer controlled multi-output RSP protocol in which one sender assists three receivers in preparing their respective target single-qubit states. In this protocol, the controllers are assigned high-, medium-, and low-level permissions. Under different multi-layer control conditions, the three receivers can reconstruct their respective original single-qubit states by performing appropriate local unitary operations. The results show that the protocol achieves unit success probability, exhibits good universality and provides a structured basis for extension to larger multi-user settings, and enforces hierarchical access control by preventing unauthorized receivers from deterministically reconstructing the target states. Subsequently, we replace the maximally entangled channel with a non-maximally entangled twelve-qubit state. After the sender performs two specific three-qubit projective measurements, the receivers can probabilistically reconstruct their respective target states under the same three-layer control structure by introducing auxiliary qubits, applying controlled-U gates, and measuring the auxiliary systems. Finally, by employing positive operator-valued measurements, the above scheme is generalized from qubit systems to arbitrary d-dimensional qudit systems, providing a theoretical basis for exploring larger multi-user quantum communication settings with hierarchical authorization.
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.