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International Journal of Quantum Information

Protocols for teleporting a cat state via a high–dimensional entangled state

Huangrui Lei, Jiangang Tang, Peng Jia-yin

Published Dec 30, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749925500406

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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 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 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 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.
Abstract We present an innovative approach for quantum teleportation (QT) in a three-dimensional (3D) quantum system, enabling the transmission of 3D quantum information from multiple senders to multiple receivers using a 3D maximally entangled GHZ-type state as a network channel.By substituting the quantum channel with a partially entangled GHZ-type state in a three-dimensional (3D) setting, we obtain an extension of the above scheme in which, when an auxiliary qubit is introduced, the receivers implement a two-particle unitary transformation and some proper 3D Weyl operators to jointly reconstruct the transmitted state with a certain probability and unit fidelity. Subsequently, inspired by the proposed schemes, a protocol for transferring a shared d-dimensional (dD) quantum state to multiple distant parties by using a dD maximally entangled GHZ-type state as quantum channel is presented, and it is generalized to the case of a dD partially entangled GHZ-type network channel by introducing an auxiliary qubit and executing a two-particle unitary transformation. Our schemes can relay quantum information over a network without requiring fully trusted central or intermediate nodes, and none of the participants can fully accesses the information.
A new scheme for short-distance quantum teleportation of an arbitrary unknown three-dimensional two-qutrit state is proposed, utilizing a three-dimensional Bell-state and a ground-state auxiliary qutrit as quantum channel. In this scheme, both the sender and receiver are required to pre-share an auxiliary qutrit in addition to sharing the three-dimensional Bell state. The sender performs joint measurements on their Bell qutrit and the unknown quantum system after performing quantum gate operations on the auxiliary qutrit, and sends the classical information of the measurement results to the receiver. Based on the measurement results, the receiver converts, with 100% probability, the quantum state of his/her own Bell qutrit and auxiliary qutrit into an exact replica of the unknown quantum state initially altered by the sender. This scheme exhibits advantages such as a short transmission distance, high information capacity, reduced consumption of entanglement resources, and promising applications in quantum teleportation for solid-state devices, such as on-chip implementations.