Sharif Digital Repository

Entanglement is one of the quantum resources that has crucial applications in many quantum tasks such as quantum teleportation, quantum key distribution, and quantum computations. Therefore, identifying entangled states is of great importance to us. There are various methods for distinguishing entangled states from separable states; however, each method is applicable under specific conditions or for special quantum states. One of these methods is measuring an observable, which, if its expectation value is negative, indicates the entanglement of the state; otherwise, it shows its separability. These observables are called entanglement witnesses, and for every entangled state, there exists at... 

It has been of great interest to know whether quantum effects can play an essential role in the biological processes. Considering that quantum features, such as coherence and entanglement,can be harnessed to perform quantum information processing tasks, which are believed to be hard classically, the question is whether nature has also exploited these features in order to enhance the performance of biological systems. Although the presence of warm and wet environment around the biological systems results in the rapid destruction of quantum effects, recent experiments reported the existence of quantum coherence in light-harvesting complexes of some photosynthetic systems.This coherence lasts... 

Physics underlies computer science because computation is a physical process. The fundamental question about computers is: What computations can be performed efficiently, and what computations are intractable? This is a question about the laws of physics and the consequences of those laws.Though we don’t know how to prove it from first principles,we have good reasons to believe that there are computational problems which are too hard to solve using digital computers based on classical physics, yet can be solved by computers which exploit quantum phenomena such as interference and entanglement. This is one of deepest distinctions ever made between classical and quantum physics, and it poses... 

Many quantum protocols that utilize entanglement are implemented between two distant bases. For various reasons, these two bases may not have a shared reference frame. In such cases, the mentioned protocols need to operate independently of the coordinate system. Therefore, identifying the entanglement of shared states between these two bases is not feasible with conventional methods, and alternative approaches must be found. The main focus of this thesis is to develop methods for identifying entangled states between two bases without the existence of a shared reference frame.
In this thesis, we begin with a comprehensive review of the history of entanglement witnesses. Next, we... 

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... 

Quantum cryptography can provide complete security. Using the quantum mechanics postulates, we can achieve a provable security which is not possible in classical cryptography. When the first completely secure protocol for distributing key was introduced, it turned a great deal of attention toward quantum cryptography and researcher focused on finding quantum mechanical counterpart of other classical cryptographic protocols. Among these protocols, quantum secret sharing is one of the most useful and important ones. In this thesis, first we introduce the basic postulates of quantum mechanics. Then, we introduce some known quantum secret sharing protocols and discuss their properties and... 

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... 

Complex systems are composed of a large number of subsystems behaving in a collective manner. In such systems, which are usually far from equilibrium, collective behavior arises due to self-organization and results in the formation of temporal, spatial, spatio-temporal and functional structures. The dynamics of order parameters in complex systems are generally non-stationary and can interact with each other in nonlinear manner. As a result, the analysis of the behavior of complex systems must be based on the assessment of the nonlinear interactions, as well as the determination of the characteristics and the strength of the fluctuating forces. This leads to the problem of retrieving a... 

Quantum computation is an unconventional way to compute employing quantum Physics. In this way of computation, quantum superposition and quantum entanglement have crucial roles to surpass common ways of computation. There is a special method for quantum computing which is known as “measurementbased quantum computation” (MBQC). In this method, sequential single-site measuring a highly-entangled state is used to perform computation. All of the existing MBQC models can be described in the “correlation space,” a virtual space corresponding to the physical space, of tensor network states. In this thesis, we introduce a recipe for designing such MBQC models. We elaborate our designing for... 

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 the last decade, the developement of Quantum Information theory have created new concepts and methods in the study of quantum many-body systems, that previously weren’t available to physicist involved in areas such as condensed matter and field theory. One of the most important steps is the insight provided by structure of the many body system’s Hilbert space. Although, it is not completed, it leads us to deep results.In fact, we have found out that with high probability, the state of a many-body system is located in a very small corner of the Hilbert space, which requires only a small number of parameteres to describe it, that with respect to the number of particles, it grows linearly...