Sharif Digital Repository

One of the main obstacles in constructing quantum computers and implementations of quantum computations and communications protocols, is the occurrence of quantum noise. In fact, due to the unavoidable interaction of the system and its surrounding environment, errors always occur and the system should be protected against noise or we need to find a way to detect the errors and correct them. Regarding the importance of the subject, intensive investigations have been done in this direction. Different approaches for correcting quantum errors are introduced. In this thesis, we focus on an approach based on collecting information from the environment. It has been shown that for a class of... 

Quantum memory which stores the coherent information of logical qubits, is an essential ingredient of quantum information processings. Each logical basis should be encoded on macroscopically distinct physical states since otherwise the indistinguishability of logical bases is easily destroyed by local errors.On the other hand, the memory must be able to have superposition of macroscopically distinct states of physical qubits. To maintain such superposition is very difficult. First, if the size of the memory is infinite, such macroscopic superposition is impossible since superposition of different phases is just a classical mixture of them in an infinite system. Second, even in finite... 

Topologically ordered phases are of great interest in the field of quantum information and quantum computation in order that their degenerate ground states provide a suitable space for coding and processing the quantum information. Such space is resistant to local errors intrinsically. A natural question to ask is to what degree these topological phases are resilient against perturbations and how the transition from topological order to another kind of order occurs.In this thesis, at first we introduce the concept of topological order. We explain the Kitaev model, which is the first introduced topological model on lattice, and study the common properties between topologically ordered systems... 

In recent studies, it has been shown that entanglement is not the only kind of genuinely quantum correlation. There exist models of quantum computation that provide exponential speed up over the best known classical algorithms and don’t have any quantum entanglement. These models show that in some cases separable state can be very useful in quantum computing models. Look for a property that causes the performance of these scenarios, quantum correlation being one of the most important concepts, including but not limited to entanglement. Local noise can produce quantum correlations on an initially classically correlated state, provided that it is not represented by a unital or semiclassical... 

Systems which have local ordered parameters are fragile and sensitive to local errors.Among these systems, quantum systems with local order face errors due to interaction with the environment, which eventuates in destruction of information. It goes without saying that quantum error-correction is a very difficult task to do. This happens in the grounds that not only is the observation of qubits impossible, but also based on no-cloning theory in quantum mechanics, there is no way to have copies of these qubits. Therefore, the interaction of quantum systems with the environment should be controlled in the way that in which we can correct errors using error-correction condition.However, there is... 

Entanglement is one of the most important concepts in quantum information science. Aer playing a significant role in the foundations of quantum mechanics, it has been discovered as a new physical resource with potential commercial applications such as teleportation, dense coding and so on. Perhaps one of the most important problems in studying the properties of entangled states is the quantification of entanglement. There are many measure of entanglement that all of them has to satis some conditions. The structure of entanglement in multipartite systems is much richer than that in the case of bipartite systems and is an open problem in quantum information theory. Graph states are special... 

Composite quantum systems are generally correlated and these correlations may have classical or quantum nature. Entanglement is only a special type of quantum correlations and separable states may be quantum correlated. Quantum discord, local quantum uncertainty and the rank of the correlation matrix are the most important measures of quantum correlations beyond entanglement. Regarding the various applications of discordant separable states in the field of quantum information, the important problem is how to produce discordant separable states and what is the resource which should be used for this preparation. In this thesis we present a method of preparation for such states in two qubit... 

Entanglement is a type of quantum correlations which due to its unique features plays a crucial role in quantum information processing. Hence trying to find new approaches in entanglement generation, distribution and also presenting strategies to optimize these processes by considering the fragility of entanglement, is always one of the most important initial steps in many quantum information processes. In this thesis we provide a systematic method to distribute entanglement by separable states and by means of separable ancilla during the process. It is worth mentioning that having separable ancilla during the process of entanglement distribution leads to more robustness against noise to... 

In most of quantum information protocols, entanglement or, in general expression, quantum correlation, plays the major role. So it is very important to know the ways of generating entanglement and protecting it against noise.
In a general view, environment is usually known as a destructive agent for entangled states. Being exposed to environment, non-diagonal elements of an entangled state’s density matrix would tend to zero, because of decoherence effect. Thus, the entanglement would be disappear. But, recent studies have shown that, this destructive agent can be convert to a useful agent for generating entanglement between system components.
In this thesis, at first, the... 

Entanglement is a type of quantum correlation that plays a crucial role at the heart of almost every quantum algorithm which has led them to outperform their classical counterparts. Recently, a new type of correlation has been introduced. Namely, ”Quantum Discord”. Which is different from the entanglement in the essence, nonetheless it has caused some quantum algorithms to outperform their classical counterparts. Since, creating and maintaining this states is easier than entangled states, they have draw many interests. In this thesis, we review and investigate the use of ”Quantum Discord” for transferring quantum information, in particular remote preparation of quantum states and Remote... 

Entanglement is one of the unique phenomena in quantum systems that does not have any similar phenomena in classical systems. Entanglement has been used in many protocols of quantum information theory, and there is agreement on its key role in quantum computations and quantum communication protocols. Therefore, studying its dynamics as well as preventing its degradation is important for us. Extensive studies have been done in this field, including the study of entanglement evolution in a situation where all parts of the system are entangled with one of its sub-system has irreversible dynamics due to interaction with its environment [1], [2], [3], [4], [5], [6], [7], [8]. However, the study... 

One of the critical subjects in quantum information science is the transmission of quantum information. Like classical channels, the question of the capacity of quantum channels arises in the quantum information theory; however, in the case of quantum information theory, there are various notions of capacities that can be defined. In quantum channels, information is encoded into the quantum degrees of freedoms, and the channels are used for the transmission of classical and quantum information. Therefore, the classical capacity and quantum capacity of quantum channels are defined as the optimal rate of the transmission of classical and quantum information through quantum channels,... 

In this thesis, our aim is to analyse the environment effects on adiabatic and non-adiabatic evolutions. In this regard, first we need to establish a suitable framework for describing the dynamics. While describing the evolution of a quantum system without interaction with its surrounding environment is easy, describing the time evolution of a quantum system in interaction with its surrounding environment is challenging. In this thesis, first we review the formalism for deriving the Markovian master equation for describing the evolution of a system in weak coupling limit. In the standard formalism, it is assumed that the system Hamiltonian is time-independent. But as our aim is to analyse... 

Currently, quantum noise stands as one of the foremost challenges in the realization of quantum algorithms and the development of quantum technologies. Consequently, finding methods to eliminate or reduce the impact of noise is imperative. This thesis explores the possibility of correcting the expectation values of observables on a quantum system, specifically a qubit quantum system experiences quantum noise, given partial knowledge of the noise. We begin by reviewing essential background information, including some of the most common methods for correcting noise, with a particular focus on the noise deconvolution technique. Subsequently, we introduce our method for correcting the... 

In this thesis, we study the divisibility of qutrit channels. First, we will review preliminaries and results in arbitrary dimensions and then results of divisibility of qubit channels. As deriving general results for Hilbert space dimension larger than two is complicated or impossible, in the following we analyze the divisibility of group-covariant channels and in particular study Z_2-covariant channels. Then we focus on qutrit channels. As there is no complete characterization of qutrit channels space, we study a subset of unital qutrit channels with the diagonal affine matrix. We call this set S and study the divisibility of its elements. First, we consider a three-parameter subset of S... 

Entanglement is considered to be one of the characteristic traits of quantum mechanics. Besides it plays a key role in quantum information science, being a resource for most of its applications such as quantum communication and quantum computation. The characterization (of different forms) of entanglement and its quantification play a central role in developing entanglement theory. By considering this fact, we describe a method for finding polynomial invariants under LOCC for a system of delocalized fermions shared between different parties, with global particle-number conservation as the only constraint. These invariants can be used to construct entanglement measures for different types of... 

One of the main aspects of resource theory is finding conditions that one state can map to another state with “allowed” operations. In quantum, allowed operations are a subset of quantum channels. In quantum thermodynamics, for example, one usually asks whether a state σ can be generated from an initial state ρ via a Gibbs-preserving channel which is a special case of [2]. In 1980 Alberti and Uhlmann [2]found a condition for the existence of a quantum channel that simultaneously transforms an input-pair of states into an output-pair. This problem is addressed in resource theory[1, 3], statistical comparison[4] and etc. Since then, this problem and its generalizations[8, 23, 22, 31, 7, 6]... 

In this thesis, we will examine quantum state and entanglement transfer. Quantum state and entanglement transfer are requirements for the development of quantum technology. Transferring the output state of a quantum processor to the next processor, which can be at an arbitrary distance from the first processor, is one of the direct applications of quantum state transfer. On the other hand, entanglement transmission is a necessary prerequisite for quantum protocols. For example, preparing the entangled pair in a laboratory and transferring one share of an entangled pair to another place in order to create entanglement between different points is essential for building quantum networks. Also,...