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.

Kohn-Sham Density Matrix and the Kernel Energy Method

The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the purposes of calculation.The results from the kernels are summed according to an expression characteristic of KEM to obtain the full molecule energy.A generalization of the kernel expansion to density matrices provides the full molecule density matrix and orbitals.In this study,the kernel expansion for the density matrix is examined in the context of density functional theory(DFT) Kohn-Sham(KS) calculations.A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined,and is then converted into a normalizedprojector by using the Clinton algorithm.Such normalized projectors are factorizable into linear combination of atomic orbitals(LCAO) matrices that deliver full-molecule Kohn-Sham molecular orbitals in the atomic orbital basis.Both straightforward KEM energies and energies from a normalized,idempotent density matrix obtained from a density matrix kernel expansion to which the Clinton algorithm has been applied are compared to reference energies obtained from calculations on the full system without any kernel expansion.Calculations were performed both for a simple proof-of-concept system consisting of three atoms in a linear configuration and for a water cluster consisting of twelve water molecules.In the case of the proof-of-concept system,calculations were performed using the STO-3 G and6-31 G(d,p) bases over a range of atomic separations,some very far from equilibrium.The water cluster was calculated in the 6-31 G(d,p) basis at an equilibrium geometry.The normalized projector density energies are more accurate than the straightforward KEM energy results in nearly all cases.In the case of the water cluster,the energy of the normalized projector is approximately four times more accurate than the straightforward KEM energy result.The KS density matrices of this study are applicable to quantum crystallography.

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.

Wigner Function：from Ensemble Average of Density Operator to Its Matrix Element in Entangled Pure States

We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.

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.

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.

Methods for Derivation of Density Matrix of Arbitrary Multi-Mode Gaussian States from Its Phase Space Representation

We present a method for derivation of the density matrix of an arbitrary multi-mode continuous variable Gaussian entangled state from its phase space representation.An explicit computer algorithm is given to reconstruct the density matrix from Gaussian covariance matrix and quadrature average values.As an example,we apply our method to the derivation of three-mode symmetric continuous variable entangled state.Our method can be used to analyze the entanglement and correlation in continuous variable quantum network with multi-mode quantum entanglement states.

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.

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.

Wigner Function:from Ensemble Average of Density Operator to Its One Matrix Element in Entangled Pure States

We show that the Wigner function W = Tr(△ρ) (an ensemble average of the density operator ρ, △ is theWigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting fromquantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangledstates are defined in the enlarged Fock space with a fictitious freedom.

Memory,Time and Technique Aspects of Density Matrix Renormalization Group Method

We present the memory size,computational time,and technique aspects of density matrix renormalization group (DMRG) algorithm.We show how to estimate the memory size and computational time before starting a large scale DMRG calculation.We propose an implementation of the Hamiltonian wavefunction multiplication and a wavefunction initialization in DMRG with block matrix data structure.One-dimensional Heisenberg model is used to illustrate our study.

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.

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.

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.

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.

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.

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.

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.