Lee-Yang Zeros And Majorana’s Stellar Representation In Quantum Information

Quantum mechanics has become the core of modern physics and has been the subject marrying the theoretical and technological fields.With almost a century’s development,many burgeoning subjects emerge as the outcomes of the coalescence.Combining the most important quantum resources,such as quantum coherence,quantum entanglement,quantum Fisher information and so on,we will study their applications.The structure of this dissertation is arranged as follows.In chapter 1,we briefly introduce the history and development of quantum mechanics and cast light on some of its newest progress.Then we introduce the background of the birth of quantum metrology and highlight its milestone,and we introduce the quantum precision measurement.We also illustrate the current research core and trend in quantum metrology.In chapter 2,we introduce the quantum information and cavity-quantum electrodynamics.Fristly,we show the definition of classical Fisher information and classical Cramér-Rao theorem.Moreover,we show their quantized counterparts and four useful solving methods:spectral decompositions,commutators,anti-commutators and unitary parametrizations.We emphatically introduce the solving method of quantum Fisher information in unitary parameterized system.In Chapter 3,we discuss the quantum channels and the probe-bath systems.At the beginning of this chapter,we introduce the definition of quantum channels and show three typical.quantum channels:depolarizing channels,dephasing channels and amplitude-damping channels.Then,we review the definitions of Lee-Yang zeros,spin squeezing and concurrence,respectively.In the final part of this chapter,we propose two different types of Lee-Yang dephasing channels,where the partition functions vanish at Lee-Yang zeros,and study the spin squeezing under them.Under the first type of the channels where probes are coupled to their own bath,we find that the performance of spin squeezing is improved and its maximum only depends on the initial state.Moreover,the centers of all the concurrence vanishing domains are corresponding to the Lee-Yang zeros.Under the second type of the channel where probes are coupled to one bath together,the performance of spin squeezing is not improved,however,the concurrence shares almost the same properties under both channels.These results provide new experimental possibilities in many-body physics and extend a new perspective of the relationship between the entanglement and spin squeezing in probes-bath systems.In chapter 4,we investigate the Majorana stellar representation in the mixed-spin(s,1/2)systems.Fristly,we introduce the background of the Majorana stellar representation.Then,we present a practical method to resolve the problem for the mixed-spin(s,1/2)system and describe the entanglement of the system.The system can be decomposed into two spins:spin-(s+1/2)and spin-(s-1/2)at the coupling bases,which can be regarded as independent spins.Besides,any pure state may be written as a superposition of two orthonormal states with one spin-(s+1/2)state and the other spin-(s-1/2)state.Thus,the whole initial state can be regarded as a state of a pseudo spin-1/2.In this way,the mixed spin decomposes into three spins.Therefore,the state can be represented by(2s+1)+(2s-1)+1＝4s+1 sets of stars on a Bloch sphere.Finally,the examples,mixed-spin(1/2,1/2)and(1,1/2)systems,are given to show symmetric patterns on the Bloch sphere and unveil the properties of the high-spin system by analyzing the trajectories of the Majorana stars on the Bloch sphere.In chapter 5,employing the quantum Fisher information as a powerful tool,we study the time-reversal protocol to sense small displacements of the light field,and report the sensitivity of our scheme that can surpass the standard quantum limit and even attain the concrete Heisenberg limit.We show the holonomic unitary parametization process of our scheme and one only need to choose appropriate initial states to pursue the ultimate sensitivity.Our scheme may pave an experimentally feasible way to achieve Heisenberg-limited metrology with nonclassical states.In Chapter 6,we summarize the results of this article and give some further prospects.