Quantum and classical correlations for a two-qubit X structure density matrix

We derive explicit expressions for quantum discord and classical correlation for an X structure density matrix. Based on the characteristics of the expressions, the quantum discord and the classical correlation are easily obtained and compared under different initial conditions using a novel analytical method. We explain the relationships among quantum discord, classical correlation, and entanglement, and further find that the quantum discord is not always larger than the entanglement measured by concurrence in a general two-qubit X state. The new method, which is different from previous approaches, has certain guiding significance for analysing quantum discord and classical correlation of a two-qubit X state, such as a mixed state.

No-relationship Between Impossibility of Faster-Than-Light Quantum Communication and Distinction of Ensembles with the Same Density Matrix

It has been claimed in the literature that impossibility of faster-than-light quantum communication has an origin of indistinguishability of ensembles with the same density matrix. We show that the two concepts are not related.We argue that even with an ideal single-atom-precision measurement, it is generally impossible to produce two ensembles with exactly the same density matrix; or to produce ensembles with the same density matrix, classical communication is necessary. Hence the impossibility of faster-than-light communication does not imply the indistinguishability of ensembles with the same density matrix.

Secure Direct Communication Using Ensembles with the Same Compressed Density Matrix

In this paper, a quantum secure direct communication protocol using ensembles with the same density matrix is proposed. The two communication parties can realize the message transmission using this method through a quantum channel, each bit of information can be transmitted using an ensemble and read out through global measurement. The eavesdropping behavior can be detected through the channel diagnoses.

Density matrix for an electron confined in quantum dots under uniform magnetic field and static electrical field

Using unitary transformations, this paper obtains the eigenvalues and the common eigenvector of Hamiltonian and a new-defined generalized angular momentum （Lz） for an electron confined in quantum dots under a uniform magnetic field （UMF） and a static electric field （SEF）. It finds that the eigenvalue of Lz just stands for the expectation value of a usual angular momentum lz in the eigen-state. It first obtains the matrix density for this system via directly calculating a transfer matrix element of operator exp（-βH） in some representations with the technique of integral within an ordered products （IWOP） of operators, rather than via solving a Bloch equation. Because the quadratic homogeneity of potential energy is broken due to the existence of SEF, the virial theorem in statistical physics is not satisfactory for this system, which is confirmed through the calculation of thermal averages of physical quantities.

Density matrix of two interacting particles with kinetic coupling derived in bipartite entangled state representation

A density matrix is usually obtained by solving the Bloch equation, however only a few Hamiltonians＇ density matrices can be analytically derived. The density matrix for two interacting particles with kinetic coupling is hard to derive by the usual method due to this coupling; this paper solves this problem by using the bipartite entangled state representation.

Time-Dependent Density Matrix Renormalization Group Coupled with n-Mode Representation Potentials for the Excited State Radiationless Decay Rate:Formalism and Application to Azulene

We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.

Density Matrix for Mesoscopic Distributed Parameter Circuits

Under the Born-von-Karmann periodic boundary condition, we propose a quantization scheme for non-dissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix rho(q,q',beta). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T. The higher the temperature is, the stronger quantum noise the circuit exhibits.

Accurate Calculation of Equilibrium Reduced Density Matrix for the System-Bath Model:a Multilayer Multiconfiguration Time-Dependent Hartree Approach and its Comparison to a Multi-Electronic-State Path Integral Molecular Dynamics Approach

An efficient and accurate method for computing the equilibriurn reduced density matrix is presented for treating open quantum systems characterized by the systern-bath model. The method employs the rnultilayer nmlticonfiguration tirne-dependent Hartree theory for imag- inary time propagation and an importance sampling procedure for calculating the quantum mechanical trace. The method is applied to the spin-boson Harniltonian, which leads to ac- curate results in agreement with those produced by the rnulti-electronic-state path integral molecular dynamics method.

Reduced one-body density matrix of Tonks-Girardeau gas at finite temperature

With thermal Bose–Fermi mapping method, we investigate the Tonks–Girardeau gas at finite temperature. It is shown that at low temperature, the Tonks gas displays the Fermi-like density profiles, and with the increase in temperature, the Tonks gas distributes in wider region. The reduced one-body density matrix is diagonal dominant in the whole temperature region, and the off-diagonal elements shall vanish rapidly with the deviation from the diagonal part at high temperature.

Real-space parallel density matrix renormalization group with adaptive boundaries

We propose an improved real-space parallel strategy for the density matrix renormalization group(DMRG)method,where boundaries of separate regions are adaptively distributed during DMRG sweeps.Our scheme greatly improves the parallel efficiency with shorter waiting time between two adjacent tasks,compared with the original real-space parallel DMRG with fixed boundaries.We implement our new strategy based on the message passing interface(MPI),and dynamically control the number of kept states according to the truncation error in each DMRG step.We study the performance of the new parallel strategy by calculating the ground state of a spin-cluster chain and a quantum chemical Hamiltonian of the water molecule.The maximum parallel efficiencies for these two models are 91%and 76%in 4 nodes,which are much higher than the real-space parallel DMRG with fixed boundaries.

Improved hybrid parallel strategy for density matrix renormalization group method

We propose a new heterogeneous parallel strategy for the density matrix renormalization group(DMRG)method in the hybrid architecture with both central processing unit(CPU)and graphics processing unit(GPU).Focusing on the two most time-consuming sections in the finite DMRG sweeps,i.e.,the diagonalization of superblock and the truncation of subblock,we optimize our previous hybrid algorithm to achieve better performance.For the former,we adopt OpenMP application programming interface on CPU and use our own subroutines with higher bandwidth on GPU.For the later,we use GPU to accelerate matrix and vector operations involving the reduced density matrix.Applying the parallel scheme to the Hubbard model with next-nearest hopping on the 4-leg ladder,we compute the ground state of the system and obtain the charge stripe pattern which is usually observed in high temperature superconductors.Based on simulations with different numbers of DMRG kept states,we show significant performance improvement and computational time reduction with the optimized parallel algorithm.Our hybrid parallel strategy with superiority in solving the ground state of quasi-two dimensional lattices is also expected to be useful for other DMRG applications with large numbers of kept states,e.g.,the time dependent DMRG algorithms.

An optimized cluster density matrix embedding theory

We propose an optimized cluster density matrix embedding theory(CDMET).It reduces the computational cost of CDMET with simpler bath states.And the result is as accurate as the original one.As a demonstration,we study the distant correlations of the Heisenberg J_(1)-J_(2)model on the square lattice.We find that the intermediate phase(0.43≤sssim J_(2)≤sssim 0.62)is divided into two parts.One part is a near-critical region(0.43≤J_(2)≤0.50).The other part is the plaquette valence bond solid(PVB)state(0.51≤J_(2)≤0.62).The spin correlations decay exponentially as a function of distance in the PVB.

Optimizing the Computation of Many-Pair Density Matrix in VDPC

Recently an algorithm that acts the variational principle directly to a coherent-pair condensate (VDPC) has been proposed. This algorithm can avoid time-consuming projection while maintaining particle number conservation. Quickly computation of many-pair density matrix (MPDM) is one of the keys to improve the computational efficiency of VDPC algorithm. In this work, we propose a scheme that limits the energy range of block particles to the vicinity of the Fermi surface, which reduces the time complexity of computing the MPDM without losing physical details. The results show that by appropriately limiting the energy range, we can greatly reduce the number of matrix elements that need to be computed, and reducing the time required for the computation.

How Kieffer Density Matrix Formalism Aids Different Initial Time Steps, Leading to Lorentz Violations, and Breakup of Primordial Black Holes for GW Generation

A result from Kieffer, as outlined at the beginning of the article identifies two different candidates for initial time steps, delta t. We assert that this difference in time steps may be related to a specific early universe Lorentz Violation. The author asserts that the existence of early universe Lorentz violation in turn is assisting in a breakup of primordial black holes. And that also has a tie into Kieffer different time steps as outlined. And the wrap up is given in the final part of this document.

Spin density matrix forΩ−and its polarization alignment in ψ(3686)→Ω−Ω¯^(+)

We investigate the spin density matrix of Ω− in the Cartesian coordinate system of baryon-antibaryon pairs produced in e+e−annihilation.Using the helicity formalism of Jacob and Wick,we derive the expression for the spin-3/2 density matrices.Our analysis is based on the angular distribution of the process e+e−→ψ(3686)→Ω−Ω¯^(+ )in the BESIII experiment.By decomposing the polarization state of Ω− particles along different coordinate axes,we examine the polarization dependence of the cross-section.Our results demonstrate that Ω− particles exhibit varying degrees of tensor polarization along the x-,y-,and z-axes,as well as weak vector polarization and rank-3 tensor polarization along the y-axis.To the best of our knowledge,this is the first study to calculate the polarization dependence of the cross-section distributions for the annihilation process e+e−→Ω−Ω¯^(+).Our theoretical predictions are in good agreement with the experimental measurements.

Density matrix method and ultrafast processes

When femtosecond （fs） timeresolved experiments are used to study ultrafast processes, quantum beat phenomena are often observed. In this paper, to analyze the fs timeresolved spectra, we will present the density matrix method, a powerful theoretical technique, which describes the dynamics of population and coherence of the system. How to employ it to study the pumpprobe experiments and fs ultrafast processes is described. The transition of pyrazine is used as an example to demonstrate the application of the density matrix method. Recently, Suzuki＇s group have employed the 22 fs time resolution laser to study the dynamics of the state of pyrazine. In this case, conical intersection is commonly believed to play an important role in this nonadiabatic process. How to treat the effect of conical intersection on nonadiabatic processes and fs timeresolved spectra is presented. Another important ultrafast process, vibrational relaxation, which takes place in subps and ps range and has never been carefully studied, is treated in this paper. The vibrational relaxation in water dimer is chosen to demonstrate the calculation. It should be noted that the vibrational relaxation of （H20）2 has not been experimentally studied but it can be accomplished by the pump-probe experiments.

Linear Scaling Discontinuous Galerkin Density Matrix Minimization Method with Local Orbital Enriched Finite Element Basis:1-D Lattice Model System

In the first of a series of papers,wewill study a discontinuous Galerkin(DG)framework for many electron quantum systems.The salient feature of this framework is the flexibility of using hybrid physics-based local orbitals and accuracy-guaranteed piecewise polynomial basis in representing the Hamiltonian of the many body system.Such a flexibility is made possible by using the discontinuous Galerkin method to approximate the Hamiltonian matrix elements with proper constructions of numerical DG fluxes at the finite element interfaces.In this paper,we will apply the DG method to the density matrix minimization formulation,a popular approach in the density functional theory of many body Schrodinger equations.The density matrix minimization is to find the minima of the total energy,expressed as a functional of the density matrixρ(r,r′),approximated by the proposed enriched basis,together with two constraints of idempotency and electric neutrality.The idempotency will be handled with theMcWeeny’s purification while the neutrality is enforced by imposing the number of electrons with a penalty method.A conjugate gradient method(a Polak-Ribiere variant)is used to solve the minimization problem.Finally,the linear-scaling algorithm and the advantage of using the local orbital enriched finite element basis in the DG approximations are verified by studying examples of one dimensional lattice model systems.

Data Gathering in Wireless Sensor Networks Via Regular Low Density Parity Check Matrix

A great challenge faced by wireless sensor networks(WSNs) is to reduce energy consumption of sensor nodes. Fortunately, the data gathering via random sensing can save energy of sensor nodes. Nevertheless, its randomness and density usually result in difficult implementations, high computation complexity and large storage spaces in practical settings. So the deterministic sparse sensing matrices are desired in some situations. However,it is difficult to guarantee the performance of deterministic sensing matrix by the acknowledged metrics. In this paper, we construct a class of deterministic sparse sensing matrices with statistical versions of restricted isometry property(St RIP) via regular low density parity check(RLDPC) matrices. The key idea of our construction is to achieve small mutual coherence of the matrices by confining the column weights of RLDPC matrices such that St RIP is satisfied. Besides, we prove that the constructed sensing matrices have the same scale of measurement numbers as the dense measurements. We also propose a data gathering method based on RLDPC matrix. Experimental results verify that the constructed sensing matrices have better reconstruction performance, compared to the Gaussian, Bernoulli, and CSLDPC matrices. And we also verify that the data gathering via RLDPC matrix can reduce energy consumption of WSNs.

Influence of matrix physical properties on flow characteristics in dual network model

The tight oil formation develops with microfractures and matrix pores,it is important to study the influence of matrix physical properties on flow characteristics.At first,the representative fracture and matrix samples are selected respectively in the dual media,the fracture and matrix digital rocks are constructed with micro-CT scanning at different resolutions,and the corresponding fracture and matrix pore networks are extracted,respectively.Then,the modified integration method is proposed to build the dual network model containing both fracture and matrix pore-throat elements,while the geometric-topological structure equivalent matrix pores are generated to fill in the skeleton domain of fracture network,the constructed dual network could describe the geometric-topological structure characteristics of fracture and matrix pore-throat simultaneously.At last,by adjusting the matrix pore density and the matrix filling domain factor,a series of dual network models are obtained to analyze the influence of matrix physical properties on flow characteristics in dual-media.It can be seen that the matrix system contributes more to the porosity of the dual media and less to the permeability.With the decrease in matrix pore density,the porosity/permeability contributions of matrix system to dual media keep decreasing,but the decrease is not significant,the oil-water co-flow zone decreases and the irreducible water saturation increases,and the saturation interval dominated by the fluid flow in the fracture keeps increasing.With the decrease in matrix filling domain factor,the porosity/permeability contributions of matrix system to dual media decreases,the oil-water co-flow zone increases and the irreducible water saturation decreases,and the saturation interval dominated by the fluid flow in the fracture keeps increasing.The results can be used to explain the dual-media flow pattern under different matrix types and different fracture control volumes during tight oil production.

Heterogeneous sensors data fusion method based on peak picking in probability density space

The multi-sensor multi-target localization and data fusion problem is discussed, and a new data fusion method called joint probability density matrix （JPDM） has been proposed, which can associate with and fuse measurements from spatially distributed heterogeneous sensors to produce good estimates of the targets. Based on probabilistic grids representation, the uncertainty regions of all the measurements are numerically combined in a general framework. The NP-hard multi-sensor data fusion problem has been converted to a peak picking problem in the grids map. Unlike most of the existing data fusion methods, the JPDM method does not need association processing, and will not lead to combinatorial explosion. Its convergence to the CRB with a diminishing grid size has been proved. Simulation results are presented to illustrate the effectiveness of the proposed technique.