Entanglement, according to the physicist Erwin Schrdinger, the essence of Quantum Mechanics, has been known for a long time now to be the source of paradoxes. The most remarkable one is called non-locality and it is at the heart of the Einstein-Podolsky-Rosen (EPR) paradox and of the fact that Quantum Mechanics violates Bell’s inequalities. Recent years, entanglement has emerged as the resource that makes quantum information science so successful. Indeed, based on entanglement, various informational tasks become feasible while they would be impossible using classical physics. Following this new trend in quantum information science, a growing community of scientists has started to investigate the resource entanglement, quantum algorithms, and the possibility of building a quantum computer that perform the quantum algorithms. However, the issue of quantum state interacting with the environment causes errors in the process of quantum computation. These errors arise mainly from decoherence, or the tendency of a quantum computer to decay from a given quantum state into an incoherent state as it interacts with the adjacent state of the environment. These interactions between the environment and quantum bits are unavoidable, and induce the breakdown of information stored in the quantum computer, and thus ended up with errors in computation. In order for quantum computer to be used to solve problems, decoherence and other potential sources of error must be reduced to an acceptable level. In this thesis, we study the various measures for quantifying bipartite and multipartite quantum entanglement for pure and mixed states. We look into the implementation of a quantum network as a universal quantum estimator where its use for estimation of state purity and entanglement are discussed in the first two chapters. The following chapters focus on quantum information processing, where one of the most useful algorithms is discussed, namely the Grover search algorithm. Based on our understanding of various entanglement measures, we study how concurrence changes over Grover search iterations. We further explore the use of this algorithm and quantum Fourier algorithm for applications in the field of bioinformatics. We then review in chapter 5 the progress made in semiconductor quantum dots systems, which have been used in many implementation for quantum information processing. We look into two applications where double quantum dots system can be exploited in chapter 6, namely the quantum teleportation and quantum state transfer. We investigate the various entanglement measures in a double quantum dots system. By introducing decoherence, we identify settings where such system can be used with acceptable performance in these applications. We conclude that quantum teleportation and quantum state transfer remain possible for a large range of external magnetic field and interdot distance under mild decoherence conditions. In chapter 7, we further investigate the nearest neighbor (NN) and nextnearest neighbor (NNN) interactions in the quantum network of one dimension structure. We perform comprehensive numerical studies on the ground state concurrence of both Heisenberg XXX model and Heisenberg XX model with periodic boundary and open boundary conditions. We found that although next-nearest-neighbor interaction does not enhance entanglement in nearest-neighbor pair in Heisenberg XXX model with periodic boundary condition, for Heisenberg XXX model with open boundary condition, nearest neighbor entanglement could be enhanced by next-nearest-neighbor nteraction. This feature is also present in Heisenberg XX model both in periodic and open boundary conditions. In the last chapter, we conclude on our research and provide some outlooks into the future development of quantum network systems.
Entanglement, according to the physicist Erwin Schrdinger, the essence of Quantum Mechanics, has been known for a long time now to be the source of paradoxes. The most remarkable one is called non-locality and it is at the heart of the Einstein-Podolsky-Rosen (EPR) paradox and of the fact that Quantum Mechanics violates Bell’s inequalities. Recent years, entanglement has emerged as the resource that makes quantum information science so successful. Indeed, based on entanglement, various informational tasks become feasible while they would be impossible using classical physics. Following this new trend in quantum information science, a growing community of scientists has started to investigate the resource entanglement, quantum algorithms, and the possibility of building a quantum computer that perform the quantum algorithms. However, the issue of quantum state interacting with the environment causes errors in the process of quantum computation. These errors arise mainly from decoherence, or the tendency of a quantum computer to decay from a given quantum state into an incoherent state as it interacts with the adjacent state of the environment. These interactions between the environment and quantum bits are unavoidable, and induce the breakdown of information stored in the quantum computer, and thus ended up with errors in computation. In order for quantum computer to be used to solve problems, decoherence and other potential sources of error must be reduced to an acceptable level. In this thesis, we study the various measures for quantifying bipartite and multipartite quantum entanglement for pure and mixed states. We look into the implementation of a quantum network as a universal quantum estimator where its use for estimation of state purity and entanglement are discussed in the first two chapters. The following chapters focus on quantum information processing, where one of the most useful algorithms is discussed, namely the Grover search algorithm. Based on our understanding of various entanglement measures, we study how concurrence changes over Grover search iterations. We further explore the use of this algorithm and quantum Fourier algorithm for applications in the field of bioinformatics. We then review in chapter 5 the progress made in semiconductor quantum dots systems, which have been used in many implementation for quantum information processing. We look into two applications where double quantum dots system can be exploited in chapter 6, namely the quantum teleportation and quantum state transfer. We investigate the various entanglement measures in a double quantum dots system. By introducing decoherence, we identify settings where such system can be used with acceptable performance in these applications. We conclude that quantum teleportation and quantum state transfer remain possible for a large range of external magnetic field and interdot distance under mild decoherence conditions. In chapter 7, we further investigate the nearest neighbor (NN) and nextnearest neighbor (NNN) interactions in the quantum network of one dimension structure. We perform comprehensive numerical studies on the ground state concurrence of both Heisenberg XXX model and Heisenberg XX model with periodic boundary and open boundary conditions. We found that although next-nearest-neighbor interaction does not enhance entanglement in nearest-neighbor pair in Heisenberg XXX model with periodic boundary condition, for Heisenberg XXX model with open boundary condition, nearest neighbor entanglement could be enhanced by next-nearest-neighbor nteraction. This feature is also present in Heisenberg XX model both in periodic and open boundary conditions. In the last chapter, we conclude on our research and provide some outlooks into the future development of quantum network systems.
The title of the present dissertation Decoherence in Quantum Network sounds very general and all-inclusive. Indeed it embraces two topics (decoherence and quantum network) from the area of Quantum Mechanics each of which is described in all respects by a huge literature developed in the last three decades [...]. Quantum decoherence, as the name lets it mean, is the mechanism that makes a quantum system loose its coherence properties, and with them the capability of giving rise to interference phenomena or to other interesting quantum effects [...]. The key idea promoted by decoherence is the insight that realistic quantum systems are never isolated, but are immersed in the surrounding environment and interact continuously with it [...]. As an example one may consider a two-level quantum system (i.e. a quantum bit, usually shortened with a terminology from information science to \\qubit" ) in contact with a wide environment. Hence, quantum systems are open systems, and continuously interact or exchange information with an external environment whose degrees of freedom are too numerous to be monitored. The resulting correlation between the system and the environment spoils quantum coherence and brings about the transition from a pure quantum state to a mixture of quantum state resulting a classical state. To describe decoherence different kind of approaches can be used (for example Master equation, random matrix, etc). A quantum network typically consists of a number of quantum objects (e.g., atoms, ions, quantum dots, cavities, etc.), to be referred to hereafter as the sites or the nodes of the network. They can interact and the interactions (or their correlations) will be usually described by the edges of a graph. Quantum networks can address different information processing tasks. For instance a quantum state can be transferred from qubit to qubit down a chain solely due to the interactions, that is according to the laws of quantum physics [...]. Quantum networks offer us new opportunities and phenomena as compared to classical networks. An extension to large scale of the idea of a quantum network could lead to a futurible quantum internet [...]. The study of networks has traditionally been the territory of graph theory [...], also with the advent of their quantum versions. Within simple quantum network model information processing is usually described by assuming perfect control of the underlying graph. However, this is not much realistic since randomness is often present and it leads to decoherence effects [...]. In contrast, the conservation of coherence is essential for any quantum information process [...], hence there is a persistent interest in decoherence effects in quantum networks, which motivate us to study models for describing such noisy effects. We consider a simple model of quantum network, employing qubits (spin-1/2 particles) attached to the nodes of an underlying graph and we study the simplest task, namely information storage (on a single and two qubits), when the graph randomly changes in time. Actually we randomly add edges to an initially disconnected graph according to the Gilbert model characterized by a weighting parameter ex [...] and in an identically and independent way at each time step. We find that by increasing ex the dynamics of relevant quantities like fidelity, entropy or concurrence, gradually transforms from damped to damped oscillatory and finally to purely oscillatory. That leads to the paper [see, Information dissipation in random quantum networks, by U. Farooq and S. Mancini, OSID 21(3), 1450004, 2014]. We also study a system composed by pairs of qubits attached to each node of a linear chain, a model that stems from quantum dot arrays. Here we use the approach of evolution with a stochastic Hamiltonian to describe the noisy effects. We then evaluate the effect of two most common disorders, namely exchange coupling and hyperfine interaction fluctuations, in adiabatic preparation of ground state in such model. We show that the adiabatic ground state preparation is highly robust against these disorders making the chain a good analog simulator. Moreover, we also study the adiabatic information transfer, using singlet-triplet states, across the chain. In contrast to ground state preparation the transfer mechanism is highly affected by disorders. This suggested that for communication tasks across such chains adiabatic evolution is not as effective and quantum quenches would be preferable. That leads to the paper [see, Adiabatic many-body state preparation and information transfer in quantum dot arrays, by U. Farooq, A. Bayat, S. Mancini and S. Bose Phys. Rev. B 91, 134303, 2015]. The present work is organized as follows. In chapter 1, we shall give a survey of the various types of approach which can be employed to analyse the dynamics of open quantum systems that leads to decoherence effects. In chapter 2, we shall give a general description about quantum network and its possible applications. In chapter 3, we shall discuss the problem of quantum state transfer in qubit network and shall give a brief overview of some scheme that enable nearly prefect state transfer. In chapter 4, we shall discuss singlet-triplet networks, that is networks having on each site a pair of (generally entangled) qubit. Then within this framework we propose a model stemming from quantum dot array. There we shall address the problem of ground state preparation and state transfer. Finally we shall describe the inherent entanglement of the ground state of strongly correlated systems can be exploited for both classical and quantum communications. In chapter 5, we shall propose a decoherence model for qubit networks based on edges representing XY interactions randomly added to a disconnected graph accordingly to a suitable probability distribution. In this way we shall describe dissipation of information initially localize in single or two qubits all over the network. In chapter 6 we shall model the noisy effects in the quantum dot array introduced in chapter 4 and investigate their consequences on the preparation of ground state and quantum state transfer mechanism. Finally we shall draw conclusions.
Quantum entanglement is a peculiar phenomenon in quantum information science, characterized by nonclassical correlations between quantum states of subsystems in a quantum system. Since the proposal of the Einstein-Podolsky-Rosen (EPR) paradox by Einstein, Podolsky, and Rosen, quantum entanglement has sparked intense debates on local realism. Bell’s inequality experiment established the nonlocality of quantum mechanics. Currently, high-dimensional quantum entanglement of both deterministic and random states can be realized in systems such as photons and cold atoms. Technologies such as quantum teleportation, quantum teleportation, quantum computing, and others rely on quantum entanglement to achieve effects beyond classical limitations. Current research focuses on the implementation of macroscopic quantum entanglement and its significance in fundamental problems of quantum mechanics. Quantum entanglement opens up a new paradigm for information processing with broad application prospects. It is necessary to conduct in-depth research on the nature of quantum entanglement and its advantages in information processing. This paper reviews the theoretical foundations of quantum entanglement, methods of generation and detection, and research progress in its applications in the field of quantum information. It discusses the important applications of quantum entanglement in quantum communication, computing, and sensing and provides an outlook on the future development prospects of quantum entanglement technologies.
Quantum information science has grown from being a very small subfield in the 70s until being one of the most dynamic fields in physics, both in fundamentals and applications. In the theoretical section, perhaps the feature that has attracted most interest is the notion of entanglement, the ghostly relation between particles that dazzled Einstein and has provided fabulous challenges to build a coherent interpretation of quantum mechanics. While not completely solved, we have today learned enough to feel less uneasy with this fundamental problem, and the focus has shifted towards its potential powerful applications. Entanglement is now being studied from different perspectives as a resource for performing information processing tasks.\n\n\t\t\t\t With bipartite entanglement being largely understood nowadays, many questions remain unanswered in the multipartite case. The first part of this thesis deals with multipartite entanglement in different contexts. In the first chapters it is studied within the whole corresponding Hilbert space, and we investigate several entanglement measures searching for states that maximize them, including violations of Bell inequalities. Later, focus is shifted towards hamiltonians that have entangled ground states, and we investigate entanglement as a way to establish a distance between theories and we study frustration and methods to efficiently solve hamiltonians that exhibit it.\n\n\t\t\t\t In the practical section, the most promised upcoming technological advance is the advent of quantum computers. In the 90s some quantum algorithms improving the performance of all known classical algorithms for certain problems started to appear, while in the 2000s the first universal computers of few atoms began to be built, allowing implementation of those algorithms in small scales. The D-Wave machine already performs quantum annealing in thousands of qubits, although some controversy over the true quantumness of its internal workings surrounds it. Many countries in the planet are devoting large amounts of money to this field, with the recent European flagship and the involvement of the largest US technological companies giving reasons for optimism.\n\n\t\t\t\t The second part of this thesis deals with some aspects of quantum computation, starting with the creation of the field of cloud quantum computation with the appearance of the first computer available to the general public through internet, which we have used and analysed extensively. Also small incursions in quantum adiabatic computation and quantum thermodynamics are present in this second part.
Information is a physical. Physical systems register and process information. These facts generated enormus interest in the development of novel quantum tecnologies, especially because the construction of smaller electronic devices ultimately leads to a consideration of quantum mechanical effects in electronic and computer desingns. The notion of the classical bit of information theory was formally pushed into the realm of the quanta with the introduction of the quantum bit or qubit, in the seminal works of Deutsch (Deutsch, 1985) and Shor (Shor, 1994). They demostrated that, indeed, controlled multipartite qubit interference effects could provide the means for a radical new way of computing, allowing the computation of many intractable computational problems, such as the factoring of large number or exact simulation of large quantum systems. The field of experimental and theoretical research in quantum information and computation has emerged as very important player in the understanding of quantum phenomena the both the basic and technological levels. This has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineerin, to the physical sciences, and we now have an interdisciplinary field where great efforts are being made in order to build devices that allow the progressing of information at a quantum level. A concise introduction to the field of quantum information and quantum computation is presented. This stars with the bassic definitions of bits, quantum registers, through to the universal gate-set for building the universal quantum computer, from a quantum network model of computation. The work shows how two-qubit gates suffice for quantum computation, emphasing the power of the quantum circuit representation for entagling and disentagling quantum states. This leads to the “no-cloning theorem”, which leads us to many interesting applications, such as quantum cryptography. Two alternative approaches or performing quantum computation are also described i) the one-way or measurement based quantum computer method, and ii) holonomic or geometric quantum computation. Following this, quantum entaglement quantification is highlighted, particulary its usefulness as a communication resource, in order to describe some of its most celebrated practical applications to date: quantum teleportation, cryptography, dens coding, and data compression. Deutsch’s concept of quantum parallelism is enphasized in order to gain insight into the potential for efficiently solving certain classically intratable algorithms. A subject central to the field of QIP- quantum decoherence- is then introduced.. Possible ways to overcome it, in particular quantum error correction, are discussed. A descriptios of some of the currently available hardware of the practical implementation of quantum computation is provided with a discussion of the main physical quantum bits that are currently employed (or proposed) for a such a purpose.
Entanglement, according to the Austrian physicist Erwin Schrödinger the Essence of Quantum Mechanics, has been known for a long time now to be the source of a number of paradoxical and counterintuitive phenomena. Of those the most remarkable one is usually called non-locality and it is at the heart of the Einstein-Podolsky-Rosen Paradox and of the fact that Quantum Mechanics violates Bell’s inequalities. Recent years saw an emergence of novel ideas in entanglement of three or more particles. Most recently it turned out that entanglement is an important concept in the development of quantum communication, quantum cryptography and quantum computation. First explicit experimental realizations with two or more photons include quantum dense coding and quantum teleportation.
Chapter devoted to the basic quantum properties of entanglement and separability. Introduces the Schmidt decomposition for pure states and the positive partial transpose criterion for mixed states as entanglement witnesses. Introduces the famous Einstein–Podolsky–Rosen paradox and its implementation in terms of qubits, then the Bell inequality, quickly reviewing the experimental demonstrations that quantum mechanics violates this inequality. Gives examples of the use of entanglement in a quantum algorithm to accelerate an information task, namely a database search (Grover algorithm) and the possibility of teleportation of a quantum state.