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.
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.
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.
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.
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.
Quantum secret-sharing is a fundamental technique in quantum communication and plays a crucial role in high-dimensional quantum secret transmission. This paper investigates the teleportation of arbitrary d-dimensional multipartite quantum secrets and proposes both deterministic and probabilistic teleportation protocols. The schemes employ generalized Bell-state measurements, generalized Pauli operators, and auxiliary particles to achieve efficient and secure quantum secret-sharing. The deterministic protocol employs maximally entangled channels to achieve perfect sharing with unit success probability. Moreover, the probabilistic protocol, assisted by auxiliary particles and generalized unitary operations, achieves perfect fidelity quantum secret sharing via non-maximally entangled channels. The protocols are further extended to arbitrary d-dimensional systems, and their robustness under several common quantum noise models is analyzed numerically. Compared with previous schemes, the proposed protocols support arbitrary multipartite entangled states, high-dimensional systems, non-maximally entangled channels, and noise analysis within a unified framework. These results enrich the theory of high-dimensional quantum communication and provide practical approaches for future quantum secret-sharing and secure quantum networks.
Very recently, Lee et al. proposed a secure quantum teleportation protocol to transfer shared quantum secret between multiple parties in a network [Phys. Rev. Lett. 124 060501 (2020)]. This quantum network is encoded with a maximally entangled GHZ state. In this paper, we consider a partially entangled GHZ state as the entanglement channel, where it can achieve, probabilistically, unity fidelity transfer of the state. Two kinds of strategies are given. One arises when an auxiliary particle is introduced and a general evolution at any receiver’s location is then adopted. The other one involves performing a single generalized Bell-state measurement at the location of any sender. This could allow the receivers to recover the transmitted state with a certain probability, in which only the local Pauli operators are performed, instead of introducing an auxiliary particle. In addition, the successful probability is provided, which is determined by the degree of entanglement of the partially multipartite entangled state. Moreover, the proposed protocol is robust against the bit and phase flip noise.
We propose a protocol for multipartite secret sharing of quantum information through an \textit{amplitude damping} quantum channel. This network is, for example, of two organizations communicating with their own employees connected via classical channels locally. We consider a GHZ state distributed among four members in an asymmetric fashion where the members of a sub-party collaborate to decode the received information at their end. The target is to send two bits of information in \textit{one execution} of the protocol. Firstly, we consider an ideal channel and observe that our protocol enables decoding of a secret 2-bit information with unit probability. This is accomplished by one of the senders by the use of a globally operated \textit{quantum teleportation operator}. Secondly, we implement the same protocol in a realistic scenario under energy dissipation by the use of a parameterized \textit{amplitude damping channel} with variable noise. This noise is associated with energy dissipation and hence, loss of probability to distinguish and decode the information at the receiving end. Finally, we make this task possible through an optimization algorithm. Various channel \textit{quality measures} are also quantitatively ascertained.