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Laser Physics Letters

Multi-output controlled teleportation of unknown single-particle states via an arbitrary high-dimensional entangled state

Ai-li Song, Nueraminaimu Maihemuti, Yimamujiang Aisan, Huang-rui Lei, Jia-yin Peng, Jian-gang Tang

Published Nov 1, 2025• 1 citation
Publisher

Abstract

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 ).

DOI
10.1088/1612-202x/ae18b5

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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 ).
This study investigates controlled bidirectional transmission of two low-dimensional unknown single-particle quantum states through high-dimensional entangled channels. Initially, complete orthogonal non-symmetric bases in [Formula: see text]-dimensional Hilbert space and five-particle maximally entangled states in d-dimensional Hilbert space are constructed, with [Formula: see text]-dimensional non-symmetric bases and 3-dimensional 5-qutrit entangled states serving as specific instances. We then propose a controlled bidirectional teleportation (CBT) protocol wherein a 3-dimensional 5-qutrit maximally entangled channel enables simultaneous exchange of two 2-dimensional single-qubit states under supervisor authorization, implemented via non-symmetric basis measurements. Subsequent replacement of the maximally entangled channel with a 3-dimensional 5-qutrit non-maximally entangled state facilitates probabilistic reconstruction of the original states through auxiliary particle introduction and appropriate unitary operations, still under supervisory control. The success probabilities are analytically derived, demonstrating that the non-maximally entangled protocol generalizes the former scheme. Furthermore, these protocols admit dual extensions: (i) quantum channel dimensionality scalable from 3-dimensional to arbitrary d dimensions; (ii) transmitted state dimensionality extendable from 2-dimensional to arbitrary f-dimensional Hilbert space (f < d).
Abstract The purpose of this paper is to explore how to teleport a low-dimensional (two-dimensional) arbitrary unknown two-qubit cat-like state through a high-dimensional entangled state constituting the quantum channel. We first present a scheme employing a maximally entangled three-qutrit state as the channel. Within this scheme, the sender performs a single-qubit projective measurement and a non-symmetric basis measurement on their particles. Based on these measurement outcomes, the receiver applies specific unitary operations to reconstruct the original cat-like state. Subsequently, the maximally entangled channel is replaced with a non-maximally entangled three-qutrit state. For this probabilistic teleportation scheme, the target state is reconstructed by introducing an auxiliary qubit and performing appropriate operations; the corresponding success probability is derived. Analysis indicates that the non-maximally entangled scheme generalizes the previous maximally entangled approach. Furthermore, both schemes are shown to be directly extendable to quantum channels formed by arbitrary high-dimensional entangled states.
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 practical quantum communication, quantum channels are inevitably affected by noise and decoherence, leading to their degradation into non-maximally entangled or even mixed states. As a result, conventional quantum teleportation schemes based on non-maximally entangled channels are inherently probabilistic and cannot simultaneously achieve unit fidelity and unit success probability. To address this issue, we exploit the structural degrees of freedom of high-dimensional partially entangled channels and construct an asymmetric joint measurement basis matched to the Schmidt-coefficient distribution of the channel, thereby proposing a controlled multi-output perfect quantum teleportation scheme. First, based on a three-dimensional partially entangled five-qutrit channel, a controlled two-output teleportation model for unknown single-qubit states is established. Perfect transmission with both unit fidelity and unit success probability is achieved through the controller’s projective measurement, the sender’s asymmetric joint measurement, and the receivers’ corresponding local recovery operations. On this basis, the scheme is generalized to arbitrary d-dimensional partially entangled channels and further extended from the two-output configuration to the multi-output scenario. Our analysis shows that, when the two largest Schmidt coefficients of the channel are equal, deterministic perfect teleportation with both unit fidelity and unit success probability can still be achieved using non-maximally entangled resources. The proposed scheme is more consistent with realistic quantum communication environments and provides a theoretical foundation for efficient and controllable quantum information distribution in complex quantum networks.
In this paper a scheme for controlled teleportation of arbitrary high-dimensional unknown quantum states is proposed by using the generalized Bell-basis measurement and the generalized Hadamard transformation. As two special cases, two schemes of controlled teleportation of an unknown single-qutrit state and an unknown two-qutrit state are investigated in detail. In the first scheme, a maximally entangled three-qutrit state is used as the quantum channel, while in the second scheme, an entangled two-qutrit state and an entangled three-qutrit state are employed as the quantum channels. In these schemes, an unknown qutrit state can be teleported to either one of two receivers, but only one of them can reconstruct the qutrit state with the help of the other. Based on the case of qutrits, a scheme of controlled teleportation of an unknown qudit state is presented.
Through a detailed study of nondestructive controlled quantum teleportation (NCQT) with two outputs in three-dimensional and high-dimensional Hilbert spaces, we propose an NCQT scheme that synchronously and probabilistically teleports N arbitrary unknown d-dimensional single-particle states from one sender to N different receivers under the supervision of a controller, by using a d-dimensional partially entangled (2N+1)-particle state as the quantum channel. The protocol succeeds if and only if all receivers recover their respective target states, and the optimal success probability of the N-output NCQT is determined by the minimum superposition coefficient of each product two-qudit state in the partially entangled channel. In our scheme, each receiver introduces an auxiliary qubit to assist in the local recovery test. When the auxiliary-qubit measurement outcome is |0⟩, the receiver can restore the target state; when the outcome is |1⟩, the corresponding unknown original state is retained by the sender. Accordingly, the N-output controlled teleportation process can be repeated as many times as additional quantum channels are available after a failed attempt. The results show that weakly entangled channels can still realize N-output controlled teleportation through sufficiently many repetitions, whereas strongly entangled channels require only a small number of repetitions to achieve the same goal.