Well-known theories like Edwards-Anderson and Sherrington-Kirkpatrick models together with some important experimental results for spin glass are introduced in chapter 1. However, there is no single model, capable of explaining all the experimental results obtained from the spin glass materials. We use the theory of quantum entanglement (concurrence) to explore the quantum correlations of a spin glass. Quantum entanglement is a useful physical resource for quantum information and communication. In chapter 2, we discuss how information is encoded and measured. The applications of quantum information in algorithms are also mentioned. As quantum information science is built upon the foundation of quantum mechanics, two important aspects of this area: Einstein, Podolsky and Rosen (EPR) gedanken experiment and the Bell's inequality are introduced in chapter 3. In chapter 4, we discuss the idea of density operator, together with the use of trace and partial trace, to describe the state of the composite system. In chapter 5, a short introduction is made on the various entanglement measures. In chapter 6, the analytical calculations of the concurrence for a 3- and 4-qubit XX model are presented. The plots of concurrence with different means and standard deviations for the 3- and 4-qubit are also presented and analyzed. The concurrence of a 2-qubit system coupled to a spin glass bath of n = 2 to 4 qubits is studied in chapter 7. With an initial separable state, the 2-qubit system reached a steady state in concurrence through time evolution when it is coupled to a quantum spin glass environment. The result is general and the behavior of the concurrence is believed to be similar for n > 4. The quantum discord is used for analyzing the XX model and presented in chapter 8. In addition, the concurrence and discord for the next nearest neighbour interaction have been plotted for 3- and 4-qubit. In chapter 9, the concurrence of the probes that are attached to a spin glass is investigated by varying the external applied magnetic field and the J coupling. By using the quantum dots (qubits) as the probe, it is possible to distinguish a spin glass from a non-spin glass with the different signatures (drop and spike) in the concurrence between the probes. The derived entanglement witness for susceptibility and specific heat capacity are used to distinguish an entangled region from an unentangled region for two different spin glass alloys: LiHoxY1-xF4 and CuxMn in chapter 10. In chapter 11, the entanglement properties of the XXZ Heisenberg (with Dzyaloshinskii-Moriya interaction) and Ising transverse field spin glass models are examined with the use of concurrence for N qubits at one-dimensional level. The concurrence for both models are obtained by using the Kadanoff''s renormalization group (RG) approach. By following the RG fl ow, a first-order and second-order phase transitions are observed by varying the standard deviation of the renormalized couplings. This thesis ends with a conclusion in chapter 12 with suggestions for future research.
Well-known theories like Edwards-Anderson and Sherrington-Kirkpatrick models together with some important experimental results for spin glass are introduced in chapter 1. However, there is no single model, capable of explaining all the experimental results obtained from the spin glass materials. We use the theory of quantum entanglement (concurrence) to explore the quantum correlations of a spin glass. Quantum entanglement is a useful physical resource for quantum information and communication. In chapter 2, we discuss how information is encoded and measured. The applications of quantum information in algorithms are also mentioned. As quantum information science is built upon the foundation of quantum mechanics, two important aspects of this area: Einstein, Podolsky and Rosen (EPR) gedanken experiment and the Bell's inequality are introduced in chapter 3. In chapter 4, we discuss the idea of density operator, together with the use of trace and partial trace, to describe the state of the composite system. In chapter 5, a short introduction is made on the various entanglement measures. In chapter 6, the analytical calculations of the concurrence for a 3- and 4-qubit XX model are presented. The plots of concurrence with different means and standard deviations for the 3- and 4-qubit are also presented and analyzed. The concurrence of a 2-qubit system coupled to a spin glass bath of n = 2 to 4 qubits is studied in chapter 7. With an initial separable state, the 2-qubit system reached a steady state in concurrence through time evolution when it is coupled to a quantum spin glass environment. The result is general and the behavior of the concurrence is believed to be similar for n > 4. The quantum discord is used for analyzing the XX model and presented in chapter 8. In addition, the concurrence and discord for the next nearest neighbour interaction have been plotted for 3- and 4-qubit. In chapter 9, the concurrence of the probes that are attached to a spin glass is investigated by varying the external applied magnetic field and the J coupling. By using the quantum dots (qubits) as the probe, it is possible to distinguish a spin glass from a non-spin glass with the different signatures (drop and spike) in the concurrence between the probes. The derived entanglement witness for susceptibility and specific heat capacity are used to distinguish an entangled region from an unentangled region for two different spin glass alloys: LiHoxY1-xF4 and CuxMn in chapter 10. In chapter 11, the entanglement properties of the XXZ Heisenberg (with Dzyaloshinskii-Moriya interaction) and Ising transverse field spin glass models are examined with the use of concurrence for N qubits at one-dimensional level. The concurrence for both models are obtained by using the Kadanoff''s renormalization group (RG) approach. By following the RG fl ow, a first-order and second-order phase transitions are observed by varying the standard deviation of the renormalized couplings. This thesis ends with a conclusion in chapter 12 with suggestions for future research.
The paper reviews the entanglement behavior of a 2-qubit system in a quantum spin glass using the Heisenberg XX model and the interaction of the system with a spin glass bath environment. In the first part, we study the entanglement (concurrence) for a 3- and 4-qubit with nearest neighbor interaction. With a fixed mean and varying standard deviation for the J coupling, the concurrence is numerically plotted with temperature for the different configurations. A general formula for the concurrence is given for n qubits at low temperature. In the second part, we study the concurrence of a 2-qubit system coupled to a spin glass bath environment with n = 2 to ≥ 4 qubits. The bath sites are coupled with random J coupling and varying applied magnetic field. A general formula for concurrence is given for mean J = 0 and B = 0 for n bath sites. For small random J and magnetic field B, a steady state is obtained with an approximate concurrence of 0.5, showing that the entanglement is preserved.
We study entanglement and discord in spin glass. By using the Edwards–Anderson XX model, we consider the Hamiltonian for three and four particles for nearest neighbor and next nearest neighbor interactions and to solve for the entanglement through concurrence. With a fixed mean and changing variances for the coupling J , the concurrence and discord are numerically plotted against the temperature. For J = 1, the critical temperature is found to be 2.106. The entanglement was found to increase beyond the critical temperature as the variance increases. The spin–spin correlation for three particles is plotted as a function of temperature T .
The thesis started with a short introduction about my research work and discussed about the systems I worked on. Later, it discussed about the experimental techniques that I have learned during the course of my work. This chapter includes the experimental approaches that I have used in sample preparation, characterization and measurements that I performed on my samples. In third chapter, I introduced about my first research work i.e. experimental quantification of entanglement in CN using magnetic susceptibility and heat capacity. In the fourth chapter, I briefly discussed about the magnetic field and temperature dependence of entanglement estimated using heat capacity. A good agreement with the theoretical predictions of our experimental results was also discussed. The fifth chapter consists of experimental study of quantum discord in CN quantified using magnetic susceptibility and heat capacity. In this chapter also I have discussed that our experimental results exhibits good correspondence with theoretical predictions and earlier reported results. In the sixth and last chapter of my thesis, I have discussed an experimental study we performed to investigate the magnetic properties of NiCr2O4 nanoparticles. Our experimental results have shown development of 2D spin-glass like phase in the nanoparticles of NiCr2O4. The parameter values we obtained by fitting the experimental data with the existing theoretical model for spin-glasses matches well with the reported values.
This thesis studies four related projects: tuning entanglement for spin systems, de-coherence and dynamics of entanglement, entanglement as measure of electron correlation in chemical systems and quantum algorithms to search for global minima. Chapter 1 presents a general introduction and the motivation for these research areas. It is composed of a brief review of the history and the future of modern computers and the state-of-art areas in quantum computation and information. Chapter 2 will be dedicated to introducing the concept of entanglement, its importance, quantification and applications. Then in Chapter 3, the properties of a set of localized spins, which are coupled to an external magnetic field through exchange interaction, are investigated. It is shown that entanglement can be controlled and tuned by varying the anisotropy parameter in the Hamiltonian, and by introducing impurities into the systems. Furthermore, the scheme for amplifying the internal entanglement by external interaction is also studied. In Chapter 4, the applications of the entanglement concept for de-coherence and dynamics is considered. In particular, the dynamics of entanglement for one-dimensional spin systems, which are coupled through nearest neighbor exchange interaction and subject to an external time-dependent magnetic field, is investigated. Using the two-site density matrix, the time-dependent entanglement of formation between nearest neighbor qubits is calculated. It is found that the entanglement can be localized between nearest neighbor qubits for certain values of the external time-dependent magnetic field. In quantum chemistry calculations, the correlation energy is defined as the difference between the Hartree-Fock limit energy and the exact solution of the non-relativistic Schrödinger equation. In Chapter 5, the application of entanglement as an alternative measure of the electron correlation in quantum chemistry calculations is proposed. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics. Finally, Chapter 6 presents the latest research results in developing quantum algorithms for searching the global minima. In this Chapter, the modified Grover’s quantum algorithm using modest numbers of quantum bits to find a global minimum for real problems is demonstrated.
Non-relativistic quantum mechanics have proven to be a significant framework to understand the non-classical behaviour of light and the microcosmos. Perhaps, one of the first technological revolutions within quantum theory came with the invention of the transistor, whereby a purely quantum mechanical description was required. Currently, another outstanding revolution is taking place in a crossroad where information science meets quantum mechanics (this being the quantum information field). Such an area of work contemplates both the fascinating theoretical aspect of quantum correlations, as well as implementations towards quantum tasks performed by a universal quantum computer; tasks that cannot be realised (or they are hard to implement) within the classical domain. This Thesis is devoted to study the dynamics of quantum entanglement in spin-optomechanics systems. In particular, we explore the quantum stabilization of quantum entanglement, a quantum concentration scheme in opto-mechanics and an interfacing of matter and light towards quantum networking applications. Additionally, we also investigate theoretical aspects of quantum correlations within thermal environments, as well as the topical area of quantum sudden transitions. In Chapter 1, we provide a brief summary of quantum information and of the quantum optics framework to cover elementary concepts and techniques used subsequently in this work. Subsequently, in Chapter 2 we present the stabilization of quantum entanglement in a non-linear qubit-oscillator system. The inclusion of a modest nonlinearity gives three results, i) the loss of periodicity of the system, ii) the occurrence of quadrature squeezing appearing for a short time, and iii) the quantum entanglement reaches higher values in contrast to the case without non-linearity. In Chapter 3, a technique to concentrate/distill a two-mode vacuum state in optomechanics via unsharp measurements is presented. Here, one of the optical modes is injected into a cavity at first, and thereafter, it is nonlinearly coupled to a mechanical oscillator. Afterwards, the position of the oscillator is measured using pulsed optomechanics and homodyne detection. The results show that this measurement can conditionally increase the initial entanglement. Next, in Chapter 4, stimulated by optomechanical transducers and quantum networking, a light-matter system is constructed where a qubit is coupled to a cavity mode mediated through a mechanical oscillator. The qubit-oscillator conditionally displaced Hamiltonian and the oscillator-cavity radiation-pressure interaction generate a maximal qubit-cavity entanglement. Additionally, we consider the case in which the cavity mode is coupled to a waveguide, numerical calculations show a promising qubit-fibre entanglement under a weak matter-light coupling. For the quantum network case, we coupled a generic qubit in the first node to a second qubit-cavity distant Jaynes-Cummings system coupled through an optical fibre, where qubit-qubit correlations can be achieved in the quantum open systems scenario. In Chapter 5, we study the evolution of an open quantum system within the Born-Markov microscopic master equation (MME). Essentially, two distant two-level atoms are trapped in fibre-coupled cavities. Under the approximation of one-excitation allowed in the atom-cavity-fibre basis, we can obtain quantum correlations induced by thermal fluctuations from the environments. Lastly, in Chapter 6, we bring together previously elements explored in this Thesis. The system is a hybrid atomic-mechanical system formed from two remote qubits interacting with individual harmonic oscillators. This system, as in Chapter 4, explores interesting applications in quantum networking schemes. The two qubits are initially prepared in a Bell-diagonal state, and consequently the two-qubit correlations exhibit few interesting effects such as freezing, sudden changes and revivals in the evolution of the quantum entropic discord. To conclude, I summarize my findings in Chapter 7.
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.