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Laser Physics Letters

Quantum teleportation of a two-qubit cat-like state via an arbitrary high-dimensional entangled state

Huangrui Lei, Jiangang Tang, Jiayin Peng

Published Sep 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1612-202x/ae027e

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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.
This study advances economical Quantum Teleportation (QT) schemes for cat states across arbitrary dimensional Hilbert spaces. First, we develop a protocol for teleporting an unknown two-dimensional cat state using a three-dimensional maximally entangled three-qutrit quantum channel. The approach involves constructing a complete orthogonal nonsymmetric measurement basis, where the sender performs joint measurements on three particles. The receiver then applies dimension-specific unitary operations conditioned on measurement outcomes to reconstruct the target state. Subsequently, we extend this protocol by replacing the maximally entangled channel with a nonmaximally entangled three-qutrit state. Through auxiliary qubit introduction and optimized operations, the two-qubit cat state is probabilistically recovered. We derive the success probability for both protocols, demonstrating that the nonmaximally entangled case generalizes the former scheme. Further generalization is achieved through two nonsymmetric basis constructions: (i) Scaling quantum channel dimension from 3 to [Formula: see text] dimensions; (ii) Extending transmitted cat states from 2 to [Formula: see text] dimensions [Formula: see text]. These dual-dimensional generalizations establish distinct economical advantages over existing QT schemes.
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 ).
We propose a quantum teleportation scheme for transmitting a single qutrit state by adopting a 2-qudit entangled state as the quantum channel. The measurement basis for Alice has been carefully and systematically constructed, which is essential for the successful implementation of the teleportation protocol. Based on Alice's measurement outcomes, we design the corresponding collective unitary transformations to be performed by Bob on an auxiliary qubit and information particle. After implementing the collective unitary transformation, Bob performs a von Neumann measurement on the auxiliary qubit. The single qutrit state is then teleported to the distant receiver Bob with a finite success probability. We obtain the achievable success probabilities of the proposed teleportation scheme for different quantum channels. The obtained results not only enrich the theory of quantum teleportation over high-dimensional entangled channels but also provide a novel and feasible approach to implementing qutrit teleportation.
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).
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.
Quantum teleportation is a unique quantum information processing method in quantum communication. Researchers have shown considerable interest in hierarchically controlled teleportation by using quantum entangled states as the quantum channel. Protocols for the hierarchically controlled teleportation of an arbitrary single-qubit via a four-qubit χ state and a four-qubit cluster state have been proposed. We present a protocol for the hierarchically controlled teleportation of an arbitrary m-qudit (d-dimensional quantum system) state by using a partially entangled quantum state as the quantum channel. The sender performs m generalized Bell-state measurements on her 2m particles. To reconstruct the original state, the upper-grade receiver only needs to apply a unitary operation in accordance with one of the receivers’ measurement results, and the lower-grade receivers need to perform a unitary operation according to all the other receivers’ measurement results. The receivers can reconstruct the original state probabilistically by introducing an auxiliary qubit and performing a collective unitary transformation. The protocol has the advantage of having high channel capacity by using a high-dimensional entangled state as the quantum channel.