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#### A Review of Quantum Uncertainty Principle and Some of Its Consequences

, M.Sc. Thesis Sharif University of Technology ; Rezakhani, Ali (Supervisor)
Abstract

In quantum mechanics, every system is described by a state function. The state function determines the probability of different outcomes of a certain measurement which is performed on the physical system. The connection between uncertainties about different measurements is presented by inequalities best known as Heisenberg’s uncertainty inequality. In face, the uncertainty relations state that there exist incompatible measurements, to which the outcomes of measurements cannot be predicted simultaneously. Although the uncertainty relations can be inferred from mathematical formalism of quantum mechanics, there is a profound relationship with other aspects of physics. Here we investigate the...

#### Dynamical Behavior in Statistical Mechanics of Open Quantum Systems

, M.Sc. Thesis Sharif University of Technology ; Rezakhani, Ali (Supervisor)
Abstract

A fundamental question in investigating decoherence and equilibrium of a system in contact with a bath is how its entropy changes in time. Normally, von Neumann’s entropy is used in such studies to quantize degree of decoherence. Recently, certain researches have been conducted addressing entropy rate and various bounds have been achieved for this quantity, utilizing which one can discuss decoherence rate and equilibrium state of open systems.In this thesis, we introduce these bounds and try to improve them. Using improved bound we will show that for almost all conceivable initial states of the system and the bath, average of entropy rate will be negligible. This result is obtained under...

#### Quantum Estimation: Properties and Calculation of the Quantum Fisher Information and Adaptive Scheme

, Ph.D. Dissertation Sharif University of Technology ; Rezakhani, Ali (Supervisor)
Abstract

In this thesis , we study quantum estimation , its primary tools and different approaches . To this end , along with reviewing the main concepts of classical and quantum estimation , the Cramer-Rao inequlity which establishes a lower bound on the precision of estimation has been used . This lower bound can be calculated using the quantum Fisher information . In order to explore properties of the quantum Fisher information , we study the continuity relation of this quantity in the most general case and we calculate it for different quantum states . To underline the importance of the continuity relation , one can demonstrate an estimate of the value of the quantum Fisher information...

#### Effects of Non-Markovian dynamics on the Energy Transport Processes in a Quantum Network

, M.Sc. Thesis Sharif University of Technology ; Rezakhani, Ali (Supervisor)
Abstract

In this thesis we are going to study the effects of Non-Markovianity on the excitation energy transport(EET) and compare it with Markovian effects. We will see that the shape of a network affects its efficiency. The speed of EET in linear networks is slowed down as Non-Markovianity is increased and this in turn lowers the efficiency of linear networks in Non-Markovian regime. Finally, we compare the efficiency of different networks

#### Review of the Range of Validity of Markovian Master Equations for Harmonic Oscillators

, M.Sc. Thesis Sharif University of Technology ; Rezakhani, Ali (Supervisor)
Abstract

Quantum mechanics, in the first place, investigates systems by introducing some principals about Hilbert space, Schrodinger equation etc. which are recognized as closed quantum systems. In principal, this is not possible to separate a system from its surrounding environment. Thus, the implications of the environment on the evolution of the system must be taken into consideration. As a matter of fact, all systems are considered open in a sense that, it is interacting with another system called the environment. In such circumstances, we tend to represent a description of open quantum systems in a way that following the evolution of the total system, i.e. system and the environment, is not...

#### Review of Thermalization in Closed Quantum Systems

, M.Sc. Thesis Sharif University of Technology ; Rezakhani, Ali (Supervisor)
Abstract

For a physical system, equilibrium is defined as a state in which the values of macroscopic quantities describing the system do not change in time. We observe systems around us reaching equilibrium every day. Describing such a seemingly simple phenomena has remained as one of the important challenges in theoretical physics. So far, various explanations for thermalization (approach to equilibrium) have been offered within classical and quantum thermodynamics. In classical statistical mechanics, the microcanonical ensemble provides a suitable prediction of the thermal behavior of a closed system. In this ensemble, using ergodic hypothesis and chaos theory one can assume that all microstates...

#### Optimal Coherent Control of Quantum Dynamics: Process-Based Approach

, Ph.D. Dissertation Sharif University of Technology ; Rezakhani, Ali (Supervisor)
Abstract

One of the main tools of the developing quantum technology is making the desired quantum gates and processes in the presence of the environmental noises. In this thesis, we first derive a Markovian master equation which defines purely the time evolution of the dynamics (process matrix) of the open system rather than its state (density matrix). This master equation indeed describes the time evolution of the Choi-Jamiolkowsli matrix which is independent of the state of the system at all times including the initial state. The n, by using this master equation we provide a scheme to manipulate optimally and locally the dynamics of the open system by external coherent agents. Such scheme...

#### Analysis of Entanglement in Ladder Lattices

, M.Sc. Thesis Sharif University of Technology ; Jafari, Akbar (Supervisor) ; Rezakhani, Ali (Supervisor)
Abstract

Since concepts in quantum information theory has recently been applied to characterize states in many-body systems, we survey entanglement of the ground states in the S = 1/2 antiferromagnetic Heisenberg ladder systems and 2D square lattices. The Lancz¨os method for exact diagonalization of quantum spin models are used to ﬁnd the ground states. Moreover, eﬀect of defect in ladder on entanglement and ground state energy are studied

#### Quantum Process Tomography: A New Approach Based on Moments

, M.Sc. Thesis Sharif University of Technology ; Tayefeh Rezakhani, Ali (Supervisor)
Abstract

In this report, we have formulated a new technique for characterizing quantum optical processes based on probing unknown processes only with coherent states and simply by measuring normally-ordered moments of output states. Our method has two substantial advantages in comparison with previous methods.First, for practical purposes of uantum-optical communications and information, predicting of the classicality or nonclassicality of output states from an unknown quantum process is generally important. Because of truncation of the Hilbert space in the Fock basis and/or exploiting Klauder theorem, antecedent methods failed to carry out foretelling the [non]classicality features of the process’...

#### The Role of Quantum Coherence and Geometry on the Excitonic Energy Transfer in Photosynthetic Structures

, M.Sc. Thesis Sharif University of Technology ; Karimipour, Vahid (Supervisor) ; Rezakhani, Ali (Supervisor)
Abstract

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...

####
Measurement-based Quantum Computation in Correlation Space

,
Ph.D. Dissertation
Sharif University of Technology
;
Karimipour, Vahid
(Supervisor)
;
Rezakhani, Ali
(Supervisor)
Abstract

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...

#### Simulation of Charge Carrier Dynamics at Interface of Two Semiconductors in Photoelectrochemical Cell Using Nonadiabatic Molecular Dynamics Approach

, Ph.D. Dissertation Sharif University of Technology ; Moshfegh, Alireza (Supervisor) ; Taeifeh Rezakhani, Ali (Supervisor)
Abstract

Nowadays, the population growth and industrial development have caused pollution of air, water, and soil, which this turned into in a global challenge. Thus, replacing the running-out fossil fuels with renewable sources of energy is an important issue facing research and scientific communities. One of the methods to generate clean energy is hydrogen production through water splitting reaction inside photoelectrochemical cells using an appropriate semiconductor. Upon the light illumination, rates of charge transfer and recombination in semiconductors heterostructure (as photoanodes) are determining factors for efficiency of these cells. If electron transfer occurs faster (in a shorter time...

#### Quantum Estimation of Open Systems Using Extended Cramer-Rao Bounds

, M.Sc. Thesis Sharif University of Technology ; Rezakhani, Ali (Supervisor) ; Alipour, Sahar (Co-Advisor)
Abstract

Any physical system is characterized with some set of quantities or parameters, knowing which, is equivalent to estimation of the system. Evaluating such parameters is usually done using tomography methods. An important question to ask, is how to increase the precision of measurement, being able to do some specific set of physical operations, say, measurement?

this question is more important in parameter estimation in quantum meanical systems. It has been shown that, quantum meanics causes a fundamental limit, on precision of estimating su parameters, escribed by the so called “antum Cramér-Rao bound”.We must note that almost all quantum meanical systems are interacting with the...

this question is more important in parameter estimation in quantum meanical systems. It has been shown that, quantum meanics causes a fundamental limit, on precision of estimating su parameters, escribed by the so called “antum Cramér-Rao bound”.We must note that almost all quantum meanical systems are interacting with the...

#### Binding Energy of Multi-Partite Quantum Systems based on Quantum Thermodynamics Viewpoint

, Ph.D. Dissertation Sharif University of Technology ; Bahrampour, Alireza (Supervisor) ; Rezakhani, Ali (Supervisor)
Abstract

Examining composite quantum systems through quantum thermodynamics, we face the new concept of binding energy. In this thesis, we are going to present a general definition for binding energy in quantum systems which covers any kind of interactions. First of all, we examine the possibility of energy exchange in a quantum system using quantum thermodynamics. In this theory, energy exchanges of an open quantum system may be divided in to two portions: heat and work; due to an accepted definition, heat is the portion of energy that is supposed to change entropy, while work has no influence on that. In this research, we restrict our calculations to the systems which are thermally closed and...

#### An Investigation into Entanglement in Electrical Transport in a One-dimensional Model Using Transfer Matrix Method

, M.Sc. Thesis Sharif University of Technology ; Rezakhani, Ali (Supervisor) ; Shokri, Ali Asghar (Co-Supervisor)
Abstract

This thesis analyzes the scattering of a propagating electron from a single bound electron .The study demonstrates how the scattering of the propagating electron from the bound electron causes entanglement between two electrons. The study then considers the impact of spin-dependent scattering in the presence of Hartree and exchange potentials. In the first step, only an exchange potential is studied. Transmission coefficients are calculated for spin-flip and non-spin-flip states by solving the Hamiltonian equation in different regions, applying the continuity boundary conditions for the wave function and its derivative in each region, and using the transfer matrix method. Transmission...

#### Relation Between Correlation and Energy in Quantum Thermodynamics

, Ph.D. Dissertation Sharif University of Technology ; Rezakhani, Ali (Supervisor) ; Huber, Marcus (Supervisor) ; Jafari, Akbar (Supervisor)
Abstract

Quantum thermodynamics is a new field of study in physics, which by considering the fundamentals of statistical mechanics, open quantum system, quantum information and mesoscopic system aims at the investigation of quantum systems from a thermodynamical point of view. To achieve these aims, a better understanding of the relations between quantum and thermodynamics fundamentals is essential. Energy and correlation are two key concepts in statistical mechanics and quantum thermodynamics (and information), respectively, that studying the relation between them will shed light on the fundamentals of quantum thermodynamics. As generating any correlation in quantum systems with initial heat state...