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Location verification in wireless sensor networks (WSNs) is quite challenging in the presence of malicious sensor nodes, which are called attackers. These attackers try to break the verification protocol by reporting their incorrect locations during the verification stage. In the literature of WSNs, most of the existing methods of location verification use a set of trusted verifiers, which are vulnerable to attacks by malicious nodes. These existing methods also use some distance estimation techniques, which are not accurate in noisy channels. In this article, we adopt a statistical approach for secure location verification to overcome these limitations. Our proposed method does not rely on any trusted entities and it takes care of the limited precision in distance estimation by using a suitable probability model for the noise. The resulting verification scheme detects and filters out all malicious nodes from the network with a very high probability even when it is in a noisy channel.

In this paper, we investigate the decoherence of GHZ state under three noisy channels in non-inertial frames. The phase flip, the bit flip and the phase damping channels are considered as noisy channels, respectively. By using three-tangle $\tau$ as the measurement of entanglement, we numerically calculate the genuine tripartite entanglement of GHZ state under noisy environments in non-inertial frames. Unlike the case of phase damping channel, in the cases of the phase flip and the bit flip ones, we find that the effect of environment cannot only decay the genuine tripartite entanglement, but also revive it.

The non-unitary evolution of initial number states in general Gaussian environments is solved analytically. Decoherence in the channels is quantified by determining explicitly the purity of the state at any time. The influence of the squeezing of the bath on decoherence is discussed. The behavior of coherent superpositions of number states is addressed as well.

We compare the sensitivity of Hilbert and Bures distances between two qubits in revealing small perturbations occurring to one of the qubits. We also analyze sensitivity in revealing perturbations to noise parameter of a depolarizing channel.

Protecting the accelerated information coherence and suppressing of its decay due to the acceleration is achieved by using different noisy channels. The behavior of three different types of information; Fisher, nonlocal and local information of qubit–qutrit system is discussed. It is shown that, the estimation rate of the acceleration parameter is maximized if both subsystems are accelerated and interacted locally with their noise channels. However, if the largest subsystem is accelerated, then the estimation rate is minimized. The rate of change of the nonlocal information depends on which subsystem is accelerated. The results display that the local information is almost unaltered during the acceleration process, that is, the information is frozen. We show that the phase-flip channel represents the weak channel, where its suppressing of the decay due to the acceleration is smaller than the dephasing and depolarize of channels.

In this paper, we propose a method through which $n$-qubit states can simultaneously be bi-directionally transmitted between two users. We assume that Alice and Bob, the legitimate users, each have a $n$-qubit GHZ-like state and want to teleport it to the other party. Also, a four-qubit cluster state plays the role of the quantum channel of this bi-directional quantum teleportation. The protocol is based on the method that at first, each user, through a series of $\text{CNOT}$ gates, converts the $n$-qubit state into a single qubit and some $0$ qubits. Then, by means of the Bell state measurement and proper operation, the single qubit state is transferred over the channel between the two sides. By re-applying the $\text{CNOT}$ gates on the transmitted qubits and auxiliary $0$ states, each user reconstructs the initial GHZ-like state. Finally, we investigate the effects of some kind of noises on the density matrix of the channel due to its interaction with the environment and present a method to protect the channel against the bit-flip error.

In this chapter, we describe several fixed length coding schemes based on trellis coded quantization (TCQ) that have been developed for image transmission over noisy channels such as wireless links. In general, wireless channels are time-varying, bandwidth constrained, and error pruned. Therefore, it is desired that the images are not only appropriately coded to achieve bandwidth compression, but also coded in such a way that the coded bitstream is resilient to channel errors and robust to time-varying channel distortion and fading. The proposed schemes consist of the basic algorithm of uniform threshold TCQ (UTTCQ) and two enhanced schemes with increased computational complexity. The enhanced schemes include nonuniform threshold TCQ and UTTCQ with block classification. We demonstrate that, in the absence of channel coding, the proposed fixed length coding schemes can be designed to achieve efficient compression, error resilience, and robustness. In particular, the fixed length coding schemes will not suffer from the loss of synchronization that often causes catastrophic error effects when more efficient variable length source coding is adopted. We also present a scheme of layered transmission with unequal error protection channel coding to further improve the performance of image transmission over noisy channels.