Research on Asymmetric Controlled Cyclic Joint Remote Quantum State Preparation in Noisy Environment

We propose a new protocol for quantum teleportation (QT) which adopts the Brown state as the quantum channel. This work focuses on the teleportation of a single unknown two-qubit state via a Brown state channel in an ideal environment. To validate the effectiveness of our proposed scheme, we conduct experiments by using the quantum circuit simulator Quirk. Furthermore, we investigate the effects of four noisy channels, namely, the phase damping noise, the bit-flip noise, the amplitude damping noise, and the phase-flip noise. Notably, we employ Monte Carlo simulation to elucidate the fidelity density under various noise parameters. Our analysis demonstrates that the fidelity of the protocol in a noisy environment is influenced significantly by the amplitude of the initial state and the noise factor.

We evaluate a one-way, bidirectional, and cyclic quantum controlled teleportation with two controllers. We show that the controllers’ agreement mimics the OR logic gate, i.e., the teleportation succeeds with only one of the controllers’ cooperation, and it does not matter which one. This result is generalized to multi-way quantum controlled teleportation with N controllers. The proposed protocols are evaluated by considering a noisy environment in the form of phase-damping noise and amplitude-damping noise and the dependence of fidelity only on the decoherence rate and the initial state’s amplitude parameter were established. It is interesting to note that for the phase-damping noise case, there are states with perfect fidelity (and the entropy equal to zero) even in a noisy environment. We discuss the novelty of the proposed protocols and highlight that they can be useful if the information to be teleported needs an OR-logic-gate-like controllers’ agreement combination, which cannot be done with other existing protocols.

We present a scheme for joint remote state preparation (JRSP) of three-particle state via three tripartite Greenberger–Horne–Zeilinger (GHZ) entangled states as the quantum channel linking the parties. We use eight-qubit mutually orthogonal basis vector as measurement point of departure. The likelihood of success for this scheme has been found to be [Formula: see text]. However, by putting some special cases into consideration, the chances can be ameliorated to [Formula: see text] and 1. The effects of amplitude-damping noise, phase-damping noise and depolarizing noise on this scheme have been scrutinized and the analytical derivations of fidelities for the quantum noisy channels have been presented. We found that for [Formula: see text], the states conveyed through depolarizing channel lose more information than phase-damping channel while the information loss through amplitude damping channel is most minimal.

In this paper, we first propose a remote state preparation (RSP) scheme in the traditional sense, which accomplishes the remote preparation of a single-qubit controlled by multiple agents in the network. This triggers a new RSP scheme, by which we can remotely prepare tensor product-type quantum states controlled by one agent. After that, we generalize the above approach to the RSP scheme of multi-qubit information controlled by multiple agents in the network. In the extended scheme, as long as all agents operate faithfully, the receiver can recover all qubits of information in the original state; otherwise, the scheme fails. Such a scheme entangles quantum information in the preparation process, thus slashing the cost of such quantum resources as auxiliary qubits and local unitary operations, and, meanwhile, reducing the number of classical bits transferred among participants. Finally, we further investigate the remote preparation scheme for multiple qubit-string information under the control of multiple agents in the network.

We have proposed two deterministic remote state preparation schemes via the χ state as the entangled channel in ideal environment. In this paper, we re-investigate the schemes in seven types of noises: amplitude-damping, phase-damping, Pauli (bit-flip, phase-flip, bit-phase flip, depolaring) and collective dephasing noise. The fidelity is used to measure how close the output state with the initial state are. It is found that the fidelities are dependent on the amplitude factor, phase factor and noise parameter. Interestingly, the fidelity is irrelated to the participators’ measurement results except in the amplitude-damping and collective dephasing noise. When the prepared states are the specific two- and three-qubit states, the fidelity is periodic in the collective dephasing noise and monotonous in other noises. Moreover, the average fidelity and state-independent average fidelity are calculated to quantify the effect of noise. Among the amplitude-damping, phase-damping and Pauli noises, the Pauli noise has the greatest impact and the phase-damping noise has the smallest impact.

A theoretical scheme is proposed to implement bidirectional quantum controlled teleportation (BQCT) by using a nine-qubit entangled state as a quantum channel, where Alice may transmit an arbitrary two-qubit state called qubits $$A_1$$A1 and $$A_2$$A2 to Bob; and at the same time, Bob may also transmit an arbitrary two-qubit state called qubits $$B_1$$B1 and $$B_2$$B2 to Alice via the control of the supervisor Charlie. Based on our channel, we explicitly show how the bidirectional quantum controlled teleportation protocol works. And we show this bidirectional quantum controlled teleportation scheme may be determinate and secure. Taking the amplitude-damping noise and the phase-damping noise as typical noisy channels, we analytically derive the fidelities of the BQCT process and show that the fidelities in these two cases only depend on the amplitude parameter of the initial state and the decoherence noisy rate.

We discuss a quantum remote state preparation protocol by which two parties, Alice and Candy, prepare a single-qubit and a two-qubit state, respectively, at the site of the receiver Bob. The single-qubit state is known to Alice while the two-qubit state which is a non-maximally entangled Bell state is known to Candy. The three parties are connected through a single entangled state which acts as a quantum channel. We first describe the protocol in the ideal case when the entangled channel under use is in a pure state. After that, we consider the effect of amplitude damping (AD) noise on the quantum channel and describe the protocol executed through the noisy channel. The decrement of the fidelity is shown to occur with the increment in the noise parameter. This is shown by numerical computation in specific examples of the states to be created. Finally, we show that it is possible to maintain the label of fidelity to some extent and hence to decrease the effect of noise by the application of weak and reversal measurements. We also present a scheme for the generation of the five-qubit entangled resource which we require as a quantum channel. The generation scheme is run on the IBMQ platform.

Quantum teleportation plays a significant role in the field of quantum communication. This paper investigates quantum teleportation through a noisy environment by using GHZ state and non-standard W state as quantum channels. We analyze the efficiency of quantum teleportation by solving analytically a master equation in Lindblad form. Following the quantum teleportation protocol, we obtain the fidelity of quantum teleportation as a function of evolution time. The calculation results show that the teleportation fidelity using non-standard W is higher in comparison to GHZ state at the same evolution time. Moreover, we consider the efficiency of teleportation with weak measurements and reverse quantum measurement under amplitude damping noise. Our analysis suggests that the teleportation fidelity using non-standard W is also more robust to noise than GHZ state in the same conditions. Interestingly, we found that weak measurement and its reverse operation have no positive effect on the efficiency of quantum teleportation by using GHZ and non-standard W state in the amplitude damping noise environment. In addition, we also demonstrate the efficiency of quantum teleportation can be improved by making minor modifications to the protocol.

Due to the important role of quantum information technology in the future development of science and technology, researchers have extensively studied the preparation, characterization, and application of quantum systems. It is of great significance to further study the universality and generalization of multi-qubit entangled states. Especially in quantum communication, the actual quantum system is always affected by various noises from the environment. Noise has a significant impact on the properties of the actual quantum system, so we study the effects of noise on a prepared two-photon four-qubit state by two methods. We experimentally simulated the most common bit-flip noise in quantum systems. The law of evolution of the fidelity of two-dimensional four-qubit states and violation of the Mermin inequality and the Ardehali inequality for LR under different levels of bit-flip noise are investigated. The experimental results show that entanglement fidelity and nonlocality can be used to judge the degree of noise interference in the quantum channel and, thus, judge the security of the quantum communication channel. This judgment is of great significance for the realization of practical long-distance multi-node quantum communication.

In this paper, the technique of weak measurement is employed in order to enhance the fidelity of joint remote state preparation (JRSP) protocol under decoherence. We design a quantum circuit of joint remote preparation of a single-qubit state through a GHZ state. Then, we analytically derive the average fidelity of the JRSP protocol under four types of noise usually encountered in real-world implementations of quantum communication protocols, i.e. the phase-flip, depolarizing, amplitude-damping and bit-flip noise. Our study shows that the application of weak measurement and measurement reversal could enhance the average fidelity of the JRSP process under the influence of phase-flip, depolarizing, amplitude-damping noise for most values of the decoherence parameters. If the JRSP process suffers from the bit-flip noise, the weak measurement technique is not useful for increasing the average fidelity.

Developing quantum systems which are robust against noise are of prime importance to the realisation of quantum technologies. Without fault tolerance, we will never be able to preserve delicate quantum states for macroscopic time scales, a necessary requirement in the construction of scalable quantum computer. Topologically ordered models offer very beautiful mechanisms for preserving quantum states. In such models, quantum information is encoded globally over a degenerate topological Hilbert space which offers a natural robustness against local environmental noise. Remarkably, topological order is present in certain realistic condensed-matter systems. This provides a platform for accessing topological order in a laboratory. Moreover, considering condensed-matter systems enables us to combine topological features with other physical effects to enhance their behaviour. In this Thesis we study the physics of topologically ordered lattice models with defects. We seek practical applications of lattice defects for the realisation of a fault-tolerant quantum computer. The first result we present shows that anyonic data of point-like lattice defects, called twists, can be found by measuring the entanglement of the ground state of the host system. The data we learn relates to the capacity of a twist defect to perform quantum computational tasks. The second result in this Thesis concerns the dynamics of the qudit toric code model with line-like defects coupled to a thermal bath. We show we can entropically inspire fragile glassy dynamics in the system. Such dynamics qualitatively improve the coherence times of quantum information encoded in the ground state of the lattice. A novel way of achieving fault-tolerant quantum computation is by producing and manipulating twist defects of topologically ordered systems. In many ways, this paradigm of topological quantum computation is analogous to quantum computation using anyons. The first area of study in this Thesis extends the analogy between anyons and twists. Specifically, we show that the anyonic data of twists in Kitaev’s toric code model can be extracted

In this paper, we investigate Einstein-Podolsky-Rosen steering, Bell non-locality, first-order coherence and concurrence in the spin- $\frac {1}{2}$ Heisenberg XX model. We first quantify these quantum resources in Heisenberg spin chain model. In fact, the spin chain model will be inevitably affected by environmental noise. Then, we find the dynamical behavior, which is a interaction of two qubits and an open environment, can test the properties of quantum resources. And the influences of these parameters are investigated on quantum resources, including the coupling coefficient, temperature, magnetic field strength and the parameters of channel. Furthermore, we will get dynamical behavior of the stable state under the circumstance of BF channel. And the role of spin chains in quantum information processing can be realized. Finally, we explore the stability of coherence, steering and Bell non-locality in AD channel. These explain how to obtain the ideal quantum state by achieving the control through quantum steering and other operations under noisy environment.

The weak measurement (WM) and quantum measurement reversal (QMR) are crucial in protecting the collapse of quantum states. The idea of WM and QMR has recently been used to protect and enhance quantum correlations and universal quantum teleportation (UQT) protocols. Here, we study the quantum correlations, maximal fidelity, and fidelity deviation of the two-qubit negative quantum states developed using discrete Wigner functions with(without) WM and QMR. To take into account the effect of a noisy environment, we evolve the states via non-Markovian amplitude damping and random telegraph noise quantum channels. To benchmark the performance of negative quantum states, we calculate their success probability. We compare our results with the two-qubit maximally entangled Bell state. Interestingly, we observe that some negative quantum states perform better with WM and QMR than the Bell state for different cases under evolution via noisy quantum channels.

In this paper, we propose an explicit scheme to fully recover a multiple-qubit state subject to a phase damping noise. We establish the theoretical framework and the operational procedure to restore an unknown initial quantum state for an N-qubit model interacting with either individual baths or a common bath. We give an explicit construction of the random unitary (RU) Kraus decomposition for an N-qubit model interacting with a common bath. We also demonstrate how to use only one unitary reversal operation to restore an arbitrary state with phase damping noise. In principle, the initial state can always be recovered with a success probability of 1. Interestingly, we found that non-RU decomposition can also be used to restore some particular entangled states. This may open a new path to restore a quantum state beyond the standard RU scheme.

Entanglement distribution is important in quantum communication. Since there is no information with value in this process, purification is a good choice to solve channel noise. In this paper, we simulate the purification circuit under true environment on Cirq, which is a noisy intermediate-scale quantum (NISQ) platform. Besides, we apply quantum neural network (QNN) to the state after purification. We find that combining purification and quantum neural network has good robustness towards quantum noise. After general purification, quantum neural network can improve fidelity significantly without consuming extra states. It also helps to obtain the advantage of entangled states with higher dimension under amplitude damping noise. Thus, the combination can bring further benefits to purification in entanglement distribution.