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International Journal of Quantum Information

Conclusive bidirectional quantum teleportation of arbitrary unknown single-particle states in amplitude-damping channel

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

Published Mar 6, 2025• 9 citations
Publisher

Abstract

In this paper, two conclusive bidirectional quantum teleportation (BQT) schemes in an amplitude damping channel are put forward. These schemes, respectively, exchange two arbitrary single-qubit states and two arbitrary single-qutrit states between two users, where both users act as senders and receivers. To achieve this, the detailed procedures for using entanglement compensation in an amplitude damped channel to share pure entangled quantum states between two users are first proposed. Then, using the pure entangled four-qubit (or four-qutrit) state shared between the users as a quantum channel, the secret quantum information of each user, i.e. the single-qubit state (or single-qutrit state), is teleported to the other user. This teleportation is designed in such a way that the information can be probabilistically reconstructed by introducing an auxiliary qubit (or qutrit) and executing proper unitary transformations by the receiver. The research results indicate that, whether in single-qubit or single-qutrit state BQT schemes, the success probability of the receiver restoring secret quantum information is determined only by the smaller absolute value of the coefficients characterizing the quantum channel. Additionally, regardless of the noise intensity in the amplitude damping channel, the fidelity of each quantum state transmitted in our BQT schemes can reach 1, which is unattainable in existing BQT schemes based on noisy environments.

DOI
10.1142/s021974992550008x

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In this paper, two conclusive bidirectional quantum teleportation (BQT) schemes in an amplitude damping channel are put forward. These schemes, respectively, exchange two arbitrary single-qubit states and two arbitrary single-qutrit states between two users, where both users act as senders and receivers. To achieve this, the detailed procedures for using entanglement compensation in an amplitude damped channel to share pure entangled quantum states between two users are first proposed. Then, using the pure entangled four-qubit (or four-qutrit) state shared between the users as a quantum channel, the secret quantum information of each user, i.e. the single-qubit state (or single-qutrit state), is teleported to the other user. This teleportation is designed in such a way that the information can be probabilistically reconstructed by introducing an auxiliary qubit (or qutrit) and executing proper unitary transformations by the receiver. The research results indicate that, whether in single-qubit or single-qutrit state BQT schemes, the success probability of the receiver restoring secret quantum information is determined only by the smaller absolute value of the coefficients characterizing the quantum channel. Additionally, regardless of the noise intensity in the amplitude damping channel, the fidelity of each quantum state transmitted in our BQT schemes can reach 1, which is unattainable in existing BQT schemes based on noisy environments.
In this paper, two conclusive multiparty quantum operation sharing (QOS) schemes in amplitude damping channel are proposed to respectively share partially unknown single-qubit unitary operations and single-qutrit unitary operations from the different restricted sets. To reach this target, the detail procedures of using entanglement compensation in amplitude damped channel to share pure entangled quantum states is first proposed. Then, using the pure entangled quantum state shared between the two sender and their two agents as a quantum channel, the dealer’s secret quantum operation, i.e. partially unknown single-qubit unitary operation (or partially unknown single-qutrit unitary operation) can be remotely implemented by the dealer at any one of the locations of all the agents in such way that the unknown quantum state after being acted on by this quantum operation can be probabilistically reconstructed through introducing an auxiliary qubit and performing appropriate local operations provided that two agents collaborate together. Subsequently, the above two schemes are generalized from 2 agents to the scenario of [Formula: see text] ([Formula: see text]) agents. In addition, through our analysis, we have found that in both single-qubit and single-qutrit QOS schemes, the probability of successful recovery of the target state by the receiver after the quantum operation is solely determined by the smaller of the absolute values of the coefficients that characterize the quantum channel. This proves that, under the same amplitude damping strength, the conclusive multiparty single-qutrit QOS has a higher success probability than the single-qubit QOS.
We give the detailed processes for sharing a four-qubit pure entangled state as quantum channel in amplitude damping (AD) network channel via entanglement compensation.We propose a secure (2,2)-type quantum teleportation (QT) scheme based on this AD network channel, which allows 2-dimensional quantum information shared by 2 senders to be teleported to 2 receivers in such a way that after performing two Bell-state measurements by two senders, the original target state can be probabilistically reconstructed through introducing an auxiliary qubit and executing appropriate local unitary operations provided that all the receivers collaborate. We then extend it to the transmission of a 2-dimensional quantum secret state shared by n senders to m receivers (i.e., (n,m)-type QT of shared 2-dimensional quantum secret) from the perspectives of projective measurement, positive-operator-valued measurement (POVM) and generalized Bell-state measurement. Furthermore, we generalize the above (n,m)-type QT to the case of transmitting a shared d-dimensional quantum secret state. Our approach enables efficient and distributed quantum information relay, eliminating the need for a fully trusted central or intermediary node. The results show that our schemes achieve unit fidelity, though the success probabilities are less than 1. More interestingly, the QT protocol for high-dimensional quantum states exhibits a higher success probability than low-dimensional states under equivalent AD conditions.
A new concept of bidirectional quantum operation teleportation (BQOT) is proposed, which is essentially a union of the idea of quantum operation teleportation (QOT) and bidirectional quantum teleportation (QT). This means that Alice can transmit an unknown single-qubit unitary operation [Formula: see text] on the remote Bob’s quantum system; and at the same time, Bob can also transmit an arbitrary single-qubit unitary operation [Formula: see text] on Alice’s quantum system. In this paper, we present three BQOT schemes via different quantum channels. Furthermore, using these quantum channels, we investigate the BQOT in noisy environments, such as phase-damping noise and amplitude-damping noise. We considered the influence of the noises on the process of these three BQOT protocols through analytical derivation of the fidelity. Moreover, these three schemes are amply compared with each other from five aspects, i.e. quantum resource consumption, operation complexity, classical resource consumption, success probability and efficiency. It is found that these schemes can be realized deterministically and the first scheme is better than the other two schemes.
We first provide four new schemes for two-party quantum teleportation of an arbitrary unknown multi-particle state by using three-, four-, and five-particle states as the quantum channel, respectively. The successful probability and fidelity of the four schemes reach 1. In the first two schemes, the receiver can only apply one of the unitary transformations to reconstruct the original state, making it easier for these two schemes to be directly realized. In the third and fourth schemes, the sender can preform Bell-state measurements instead of multipartite entanglement measurements of the existing similar schemes, which makes real experiments more suitable. It is found that the last three schemes may become tripartite controlled teleportation schemes of teleporting an arbitrary multi-particle state after a simple modification. Finally, we present a new scheme for three-party sharing an arbitrary unknown multi-particle state. In this scheme, the sender first shares three three-particle GHZ states with two agents. After setting up the secure quantum channel, an arbitrary unknown multi-particle state can be perfectly teleported if the sender performs three Bell-state measurements, and either of two receivers operates an appropriate unitary transformation to obtain the original state with the help of other receiver's three single-particle measurements. The successful probability and fidelity of this scheme also reach 1. It is demonstrated that this scheme can be generalized easily to the case of sharing an arbitrary unknown multi-particle state among several agents.
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.
In this paper, two conclusive three-party cyclic assisted cloning protocols in amplitude damping (AD) channel are put forward that, respectively clone three arbitrary unknown single-qubit states and single-qutrit states with the help of a state preparer. Each of our protocols includes three consecutive stages: quantum channel preparation, cyclic quantum teleportation (CQT), and multi-party assisted cloning. The first stage of each protocol proposes the detailed processes of sharing a pure entangled quantum state as a component of a quantum channel in AD channel via entanglement compensation. In second stage, a three-party CQT is presented where three unknown single-qubit states (or single-qutrit states) are reconstructed simultaneously in three different places, respectively, by introducing auxiliary qubits and performing appropriate operations. In the third stage, the state preparer Victor performs one multi-qubit measurement (or one unitary transformation and one multi-qutrit measurement) and informs the three communicators of his outcome, three distinct unknown single-qubit states or their orthogonal complement states (or single-qutrit states) are cloned simultaneously and with probability at three separate locations,respectively. Furthermore, we extend the above protocols from two aspects: (i) the extension to the case of [Formula: see text] participants; (ii) extension to the case of d-dimensional unknown single-qudit state cycle-assisted cloning.