Quantum Correlation in Matrix Product States of One-Dimensional Spin Chains

For our proposed composite parity-conserved matrix product state (MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. Both the total correlation and the classical correlation become larger than that in any subcomponent; while the quantum correlations of the two nearest-neighbor spin blocks and the two next-nearest-neighbor spin blocks become smaller and for other conditions the quantum correlation becomes larger, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation, which deserves to be investigated in the future; and the ration of the quantum correlation to the total correlation monotonically decreases to a steady value as the spacing spin length increasing.     

Quantum Correlation in Matrix Product States of One-Dimensional Spin Chains

For our proposed composite parity-conserved matrix product state(MPS), if only a spin block length is larger than 1, any two such spin blocks have correlation including classical correlation and quantum correlation. Both the total correlation and the classical correlation become larger than that in any subcomponent; while the quantum correlations of the two nearest-neighbor spin blocks and the two next-nearest-neighbor spin blocks become smaller and for other conditions the quantum correlation becomes larger, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation, which deserves to be investigated in the future; and the ration of the quantum correlation to the total correlation monotonically decreases to a steady value as the spacing spin length increasing.     

Quantum Phase Transitions in Matrix Product States

We present a new general and much simpler scheme to construct various quantum phase transitions （Q, PTs） in spin chain systems with matrix product ground states. By use of the scheme we take into account one kind of matrix product state （MPS） OPT and provide a concrete model. We also study the properties of the concrete example and show that a kind of Q, PT appears, accompanied by the appearance of the discontinuity of the parity absent block physical observable, diverging correlation length only for the parity absent block operator, and other properties which are that the fixed point of the transition point is an isolated intermediate-coupling fixed point of renormalization flow and the entanglement entropy of a half-infinite chain is discontinuous.     

双模最小关联混态的量子统计性质

研究了双模最小关联混态在不同参数情况下的量子统计性质.发现在一定的参数范围内双模最小关联混态的二阶相干性违反经典的Cauchy-Schwartz不等式,呈现非经典性相关;同时对双模最小关联混态的压缩特性、亚泊松分布等非经典性质进行了分析,通过数值计算得出,每模光子的压缩性及其亚泊松分布均与参数d的取值密切相关.     

Critical Dynamics of Transverse-field Quantum Ising Model using Finite-Size Scaling and Matrix Product States

The study of phase transition is usually done by numerical simulation of finite system. Conventional methods such as Monte Carlo simulations and phenomenological renormalization group methods obtain the critical exponents without obtaining the quantum wavefunction of the system. The Matrix Product States formalism allows one to obtain accurate numerical wavefunctions of short ranged interacting quantum many-body systems. In this study we combine the Finite Size Scaling theory and Matrix Product States formalism to study the critical dynamics of one-dimensional quantum Ising model. Finite size simulations of 20, 40, 60, 80, 100 and 120 spins are done using the Density Matrix Renormalization Group to obtain the ground state wavefunction of the system. The thermodynamic quantities such as the magnetization, susceptibility and correlation function are calculated. The critical exponents independently calculated are respectively β/ν = 0.1235(1), γ/ν = 1.7351(2), and η = 0.249(1). They conform with the theoretical values from analytical solution and fulfil the hyperscaling relation. We showed that both methods combined can reliably study the critical dynamics of one-dimensional Ising-like quantum lattice systems. Application of the study on water-ice phase transition of single-file water in nanopores is proposed.

     

Quantum Phase Transitions in Conventional Matrix Product Systems

For matrix product states(MPSs) of one-dimensional spin-\(\frac {1}{2}\) chains, we investigate a new kind of conventional quantum phase transition(QPT). We find that the system has two different ferromagnetic phases; on the line of the two ferromagnetic phases coexisting equally, the system in the thermodynamic limit is in an isolated mediate-coupling state described by a paramagnetic state and is in the same state as the renormalization group fixed point state, the expectation values of the physical quantities are discontinuous, and any two spin blocks of the system have the same geometry quantum discord(GQD) within the range of open interval (0,0.25) and the same classical correlation(CC) within the range of open interval (0,0.75) compared to any phase having no any kind of correlation. We not only realize the control of QPTs but also realize the control of quantum correlation of quantum many-body systems on the critical line by adjusting the environment parameters, which may have potential application in quantum information fields and is helpful to comprehensively and deeply understand the quantum correlation, and the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems.     

Composite Discordant States and Quantum Darwinism

The framework of Quantum Darwinism strives at characterizing the quantum-to-classical transition by introducing the concept of redundancy of information—as measured by Mutual Information—that a set of observers would acquire on the state of a physical system of interest. Further development on this concept, in the form of Strong Quantum Darwinism and Spectrum Broadcast Structures, has recently led to a more fine-grained identification of the nature of such information, which should not involve any quantum correlations between observing and observed systems, while the assessment of information proliferation from individual systems has attracted most of the attention so far, the way such mechanism takes place in more complex states is open to exploration. To this end, we shall consider a two-qubit state, sharing initial quantum correlations in the form of Quantum Discord, and different dephasing-like interactions between them and an observing environment. We will focus on the amount of information regarding the subsystem not involved in the interaction that is proliferated to the environment. We shall refer to this as mediated redundancy. We will show that, in some cases, the channel capacity of the subsystems, given these interactions, can exceed that of the fragments.     

Reduced Density Matrix and Quantum Correlation in Two-Qubit Quantum Rabi Model

International Journal of Theoretical Physics - In this work, we give an analytical derivation of the reduced density matrix between two qubits in a cavity field, which is described by the quantum...     

Quantum Correlation Coefficients for Angular Coherent States

Quantum covariance and correlation coefficients of angular or SU（2） coherent states are directly calculated for all irreducible unitary representations. These results explicitly verify that the angular coherent states minimize the Robertson-Schrodinger uncertainty relation for all spins, which means that they are the so-called intelligent states. The same results can be obtained by the Schwinger representation approach.     

相干态与压缩态迭加的量子特性

基于量子力学基本理论,构造了一个由相干态与单模压缩态构成的新迭加态:|φ>=N(|α> eiψ|β>g);详细讨论了其压缩效应和光子数反聚束效应,发现该迭加态呈现出多样的量子特性.在按类似奇偶相干态的方式迭加时,迭加态具有奇偶相干态和压缩奇偶相干态的某些特性.作为特例,当压缩因子为0时,可以得到奇偶相干态和相干态.     

Matrix Product States, Random Matrix Theory and the Principle of Maximum Entropy

Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.     

Quantum Discord in any Mixture of Two Bi-Qubit Arbitrary Product States

Quantum discord in any mixture of two bi-qubit arbitrary product states is studied with two different approaches. In the first approach the maximM classicM correlations are obtained via numerical computations, while in the second approach they are analytically derived. Quantum correlations captured with both approaches completely coincide, as is in accord with the conclusion of Cen et al. [Phys. Rev. A 83 （2011） 054101]. The symmetry reduction of the concerned states concerning quantum correlations is accomplished. The captured discords are amply analyzed so that some inherent distinct properties are revealed.     

Quantum Discord in any Mixture of Two Bi-Qubit Arbitrary Product States

Quantum discord in any mixture of two bi-qubit arbitrary product states is studied with two different approaches. In the first approach the maximal classical correlations are obtained via numerical computations, while in the second approach they are analytically derived. Quantum correlations captured with both approaches completely coincide, as is in accord with the conclusion of Cen et al. [Phys. Rev. A 83 (2011) 054101]. The symmetry reduction of the concerned states concerning quantum correlations is accomplished. The captured discords are amply analyzed so that some inherent distinct properties are revealed.     

Thermodynamic Properties of Non-equilibrium States in Quantum Field Theory

Within the framework of relativistic quantum field theory, a novel method is established which allows for distinguishing non-equilibrium states admitting locally a thermodynamic interpretation. The basic idea is to compare these states with global equilibrium states (KMS states) by means of local thermal observables. With the help of such observables, the states can be ordered into classes of increasing local thermal stability. Moreover, it is possible to identify states exhibiting certain specific thermal properties of interest, such as a definite local temperature or entropy density. The method is illustrated in a simple model describing the spatio-temporal evolution of a “big heat bang.”     

A Secure Quantum Voting Scheme Based on Orthogonal Product States

International Journal of Theoretical Physics - As an important topic of quantum cryptography, quantum voting has attracted more and more attention in recent years. In this paper, we propose a...     

Estimating Quantum Mutual Information of Continuous-Variable Quantum States by Measuring Purity and Covariance Matrix

We derive accessible upper and lower bounds for continuous-variable (CV) quantum states on quantum mutual information. The derivations are based on the observation that some functions of purities bound the difference between quantum mutual information of a quantum state and its Gaussian reference. The bounds are efficiently obtainable by measuring purities and the covariance matrix without multimode quantum state reconstruction. We extend our approach to the upper and lower bounds for the quantum total correlation of CV multimode quantum states. Furthermore, we investigate the relations of the bounds for the quantum mutual information with the bounds for the quantum conditional entropy.