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.
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.
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.
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 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.
Abstract Our concern is to investigate controlled remote implementation of partially unknown operations with multiple layers. We first propose a scheme to realize the remote implementation of single-qubit operations belonging to the restricted sets. Then, the proposed scheme is extended to the case of single-qudit operations. As long as the controller and the higher-layer senders consent, the receiver can restore the desired state remotely operated by the sender. It is worth mentioning that the recovery operation is deduced by general formulas which clearly reveal the relationship with the measurement outcomes. For the sake of clarity, two specific examples with two levels are given respectively. In addition, we discuss the influence of amplitude-damping noise and utilize weak measurement and measurement reversal to effectively resist noise.
In this paper, we propose a novel scheme for quantum two-state sharing (QTSS) by using a five-qubit entangled state as the quantum channel. In this scheme, a dealer Alice has two unknown quantum states and wants her three agents to share the quantum states. After the dealer performs a four-qubit measurement on her qubits, and the controller employs a single-qubit measurement on his own qubit, the state receivers can reconstruct the original states by using the appropriate unitary operations. It is shown that, only if all agents collaborate with each other, the QTSS can be completed with unit success probability.
Two three-party schemes are put forward for sharing quantum operations on a remote qutrit with local operation and classical communication as well as shared entanglements. The first scheme uses a two-qutrit and three-qutrit non-maximally entangled states as quantum channels, while the second replaces the three-qutrit non-maximally entangled state with a two-qutrit. Both schemes are treated and compared from the four aspects of quantum and classical resource consumption, necessary-operation complexity, success probability and efficiency. It is found that the latter is overall more optimal than the former as far as a restricted set of operations is concerned. In addition, comparisons of both schemes with other four relevant ones are also made to show their two features, including degree generalization and channel-state generalization. Furthermore, some concrete discussions on both schemes are made to expose their important features of security, symmetry and experimental feasibility. Particularly, it is revealed that the success probabilities and intrinsic efficiencies in both schemes are completely determined by the shared entanglement.