This paper proposes a three-dimensional (3D) controlled quantum teleportation scheme for an unknown single-qutrit state. The scheme is first introduced in an ideal environment, and its detailed implementation is described via the transformation of the quantum system. Four types of 3D-Pauli-like noise corresponding to Weyl operators are created by Kraus operators: trit-flip, t-phase-flip, trit-phase-flip, and t-depolarizing. Then, this scheme is analyzed in terms of four types of noisy channel with memory. For each type of noise, the average fidelity is calculated as a function of memory and noise parameters, which is afterwards compared with classical fidelity. The results demonstrate that for trit-flip and t-depolarizing noises, memory will increase the average fidelity regardless of the noise parameter. However, for t-phase-flip and trit-phase-flip noises, memory may become ineffective in increasing the average fidelity above a certain noise threshold.
This paper proposes a three-dimensional (3D) controlled quantum teleportation scheme for an unknown single-qutrit state. The scheme is first introduced in an ideal environment, and its detailed implementation is described via the transformation of the quantum system. Four types of 3D-Pauli-like noise corresponding to Weyl operators are created by Kraus operators: trit-flip, t-phase-flip, trit-phase-flip, and t-depolarizing. Then, this scheme is analyzed in terms of four types of noisy channel with memory. For each type of noise, the average fidelity is calculated as a function of memory and noise parameters, which is afterwards compared with classical fidelity. The results demonstrate that for trit-flip and t-depolarizing noises, memory will increase the average fidelity regardless of the noise parameter. However, for t-phase-flip and trit-phase-flip noises, memory may become ineffective in increasing the average fidelity above a certain noise threshold.
Abstract The purpose of this paper is to further investigate the correlated and memory effects in 3D-Pauli-like noisy channels for controlled teleportation of an arbitrary unknown single-qutrit state. We first construct a three-qutrit maximally entangled state in a three-dimensional (3D) Hilbert space and subsequently propose a 3D controlled quantum teleportation (CQT) scheme for an arbitrary unknown single-qutrit state using the constructed three-qutrit maximally entangled state as the quantum channel. In this ideal case, through a few simple 3D unitary operations, the two communicating parties can perfectly accomplish the teleportation task under the supervision of the controller. Subsequently, we examine the performance of this CQT scheme under two successive uses of a 3D-Pauli-like noisy channel with memory, where the noise errors are categorized into four types: trit-flip, t-phase-flip, trit-phase-flip, and t-depolarizing. For each noise type, an analytical expression of the average fidelity is derived as a function of both the noise and memory parameters. Specifically, we find that, regardless of the noise strength, memory enhances the average fidelity for trit-flip and t-depolarizing noises, whereas for t-phase-flip and trit-phase-flip noises, memory reduces the average fidelity once the noise intensity exceeds a certain threshold. This indicates that in the first two noisy channels, memory can improve the communication efficiency of CQT, while in the latter two, excessive noise causes memory to diminish the teleportation performance.
A scheme is proposed for cyclic-controlled quantum operation teleportation (CCQOT) for three sides with EPR and cluster states. Under the control of David, Alice can implement an unknown single-qubit unitary operation on the remote Bob’s quantum system, while Bob can execute a single-qubit unitary operation on Charlie’s quantum system and Charlie can also perform an unknown single-qubit unitary operation on Alice’s quantum system. Our scheme can be generalized to [Formula: see text]) agents involved in the cycle to realize the transmission of single-qubit operations. Moreover, by replacing the quantum channels, we can change the cyclic direction of controlled qunatum operation teleportation (CQOT) from clockwise to counterclockwise. In addition, we discuss our scheme in four types of noisy environments (amplitude-damping, phase-damping, bit-flip and phase-flip noisy environment), and use fidelity to analyze the amount of information lost in the process of CCQOT due to noise. The results show that the fidelity is determined by decoherence rate and amplitude parameters of the final state.
Abstract We propose two novel protocols for bidirectional quantum teleportation (BQT) of qutrit states in multi-party settings: a cyclic BQT protocol enabling simultaneous state exchange among three or more users, and a controlled BQT protocol incorporating a supervisory authorization mechanism. Both protocols leverage optimized multi-qutrit entangled channels and deterministic measurement-based correction schemes. We derive exact analytical expressions for the state-independent average fidelities under all four types of three-dimensional Pauli-like noise channels: trit-flip, t-phase-flip, trit-phase-flip, and t-depolarizing. Our results demonstrate a linear fidelity degradation with noise parameter p , yet both protocols maintain superior resource efficiency and security compared to conventional two-party BQT. The cyclic protocol achieves a 33% reduction in entanglement resource consumption compared to sequential two-party implementations, while the controlled protocol ensures unconditional security against unauthorized access. These advances establish a practical framework for high-dimensional quantum networks and secure distributed quantum applications.
We study the protocol of qudit teleportation using quantum systems subjected to several kinds of noise for arbitrary dimensionality d. We consider four classes of noise: dit-flip, d-phase-flip, dit-phase-flip, and depolarizing noise, each of them corresponding to a family of Weyl operators, introduced via Kraus formalism. We derive a general expression for the average fidelity of teleportation in arbitrary dimension d for any combination of noise on the involved qudits. Under a different approach we derive the average fidelity of teleportation for a more general scenario involving the d-dimensional generalization of amplitude damping noise as well. We show that all possible scenarios may be classified in four different behaviors and discuss the cases in which it is possible to improve the fidelity by increasing the associated noise fractions. All our results are in agreement with previous analysis for the case of qubits [R. Fortes and G. Rigolin, Phys. Rev. A 92, 012338 (2015)].
In order to explore multi-directional quantum communication in a three-dimensional (3D) system, five-, seven- and [Formula: see text]-qutrit entangled states are constructed by 3D-Hadamard gates and 3D-controlled-NOT gates in this paper. Then a new scheme of controlled bidirectional quantum teleportation (QT) via five-qutrit entangled channel is proposed, where two observers can exchange their unknown single-qutrit states at the same time under the control of the supervisor. Along this mental, we propose a novel theoretical scheme to fulfil four-party controlled cyclic QT by using a seven-qutrit entangled state as the quantum channel, in which Alice can teleport an arbitrary unknown single-qutrit state to Bob, Bob can transmit an arbitrary single-qutrit state to Charlie, at the same time, Charlie can also teleport an arbitrary unknown single-qutrit state to Alice with the permission of the supervisor. In these schemes, only specific two-qutrit 3D-Bell state measurements, single-qutrit 3D-Z-basis measurements and suitable 3D-Weyl operators are needed, which can be implemented in physics easily. Moreover, the proposed four-party controlled cyclic scheme can be generalized into the case containing [Formula: see text] ([Formula: see text]) observers by using a [Formula: see text]-qutrit entangled channel. Analysis shows that the success probability of our schemes can reach 1. Through detailed discussion, we find that the security of our schemes and the control power of the supervisors can be guaranteed, and the intrinsic efficiency of the proposed schemes is relatively high.
The concept of quantum teleportation is fundamental in the theory of quantum communication. Developing models of quantum teleportation in different physical scenario is a modern trend of research in this direction. This work is at the interface of hypergraph theory and quantum teleportation. We propose a new teleportation protocol for qutrit states in a noisy environment. This protocol utilizes a shared quantum hypergraph state between parties as quantum channels, to carry quantum information. During the preparation of the shared state different quantum noise may act on it. In this article, we consider six types of noises which are generalized for qutrits using Wyel operators. They are the qutrit-flip noise, qutrit-phase-flip noise, depolarizing noise, Markovian and non-Markovian amplitude damping channel, Markovian and non-Markovian dephasing channel, and non-Markovian depolarization noise. There are only five qutrit hypergraph states which satisfies our requirements to be used as a channel. We consider all of them in this work. For different hypergraph states and different noises we work out the analytical expressions of quantum teleportation fidelity.