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Mathematics

Multi-Layer Controlled Multi-Output Remote State Preparation of Single-Particle States

Nueraminaimu Maihemuti, Yimamujiang Aisan, Peng Jia-yin, Jiangang Tang

Published Sep 2, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.3390/math14173157

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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.
Abstract We propose two schemes for realizing multi-output quantum teleportation of arbitrary unknown single-qubit and single-qudit states, respectively, under a multi-layer control structure. Nine-particle entangled quantum channels are constructed in two-dimensional and d -dimensional Hilbert spaces, and a hierarchical control mechanism is designed to enable controllers with different authorization levels to collaboratively and selectively influence the reconstruction of quantum states at multiple receivers. Firstly, based on the constructed two-dimensional nine-qubit entangled channel, a deterministic multi-layer controlled multi-output teleportation scheme is proposed and its performance is analyzed. The results show that the protocol achieves unit success probability, possesses good universality and scalability, and can effectively defend against unauthorized access and eavesdropping. Finally, the scheme is extended from qubits to arbitrary-dimensional qudits, providing theoretical support for building secure and scalable multi-user quantum communication networks.
In this paper, we propose a novel scheme for deterministic hierarchical joint remote state preparation (HJRSP). Two senders and three receivers are involved. One sender has the amplitude information of the target state to be prepared at the receiver's port, while the other one has the phase information. There is a hierarchy among the receivers concerning their powers to reconstruct the target state. 6-particle partially entangled state is used as the quantum channel. Participants perform projective measurements under elaborate measurement bases. According to their measurement results, the receiver reconstructs the target state by means of appropriate unitary operation. The higher-power receiver reconstructs the target state independently, and the lower-power receiver reconstructs the target state if and only if all the other receivers help him (her). Different from the previous HJRSP scheme utilizing partially entangled channels, auxiliary qubit is not required in our scheme, and unit success probability can be achieved. It is shown that the success probability is independent of the parameters of the partially entangled quantum channel.
In this paper, we present a novel scheme for hierarchical joint remote state preparation (HJRSP) in a deterministic manner, where two senders can jointly and remotely prepare an arbitrary single-qubit at three receivers’ port. A six-particle partially entangled state is pre-shared as the quantum channel. There is a hierarchy among the receivers concerning their powers to reconstruct the target state. Due to various unitary operations and projective measurements, the unit success probability can always be achieved irrespective of the parameters of the pre-shared partially entangled state.
In this paper, two efficient proposals are presented by using maximal slice states and orthogonal measurement basis to realize the joint remote state preparation (RSP) of two-qubit and three-qubit states, respectively. Furthermore, this kind of joint RSP schemes could be generalized to the case of arbitrary multi-qubit states, which can be transmitted from two senders to one receiver with the supervision of one manager. The successful probability of this joint RSP scheme is always equal to 100% in spite of that quantum channel is composed of non-maximally entangled states.
In this paper, two novel schemes for deterministic joint remote state preparation (JRSP) of arbitrary single- and two-qubit states are proposed. A set of ingenious four-particle partially entangled states are constructed to serve as the quantum channels. In our schemes, two senders and one receiver are involved. Participants collaborate with each other and perform projective measurements on their own particles under an elaborate measurement basis. Based on their measurement results, the receiver can reestablish the target state by means of appropriate local unitary operations deterministically. Unit success probability can be achieved independent of the channel's entanglement degree.
Abstract The purpose of this article is to explore how to transmit low-dimensional unknown single-particle states in a multi-output manner through a high-dimensional entangled state as a quantum channel under the control of a supervisor. First, we construct a set of complete orthogonal non-symmetric bases in ( d × f ) -dimensional Hilbert space and a ( 2 N + 1 ) -qudit maximally entangled state in d -dimensional Hilbert space, taking a set of ( 3 × 2 ) -dimensional non-symmetric bases and a 3-dimensional 5-qutrit entangled state as their special cases, respectively. We then propose a controlled teleportation scheme, where by using the 3-dimensional 5-qutrit maximally entangled state as a quantum channel and employing the ( 3 × 2 ) -dimensional non-symmetric basis measurement, two 2-dimensional single-qubit states are simultaneously teleported through quantum teleportation technology under the control of a supervisor. Subsequently, the above maximally entangled quantum channel is replaced by a 3-dimensional 5-qutrit non-maximally entangled state, and two unknown single-qubit states are teleported, under the control of a supervisor, in such a way that they can be probabilistically reconstructed by introducing auxiliary qubits and performing appropriate operations. The success probabilities of the above two schemes are given, and the analysis shows that the scheme based on a non-maximally entangled channel is a generalization of the previous scheme. In addition, the above schemes can be extended from the following two perspectives: (a) the quantum channels can be extended from 3-dimensional to arbitrary d -dimensional; (b) the transmitted quantum information can be extended from 2-dimensional to any f -dimensional through d -dimensional entangled quantum channels ( f < d ).