Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence o...Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.展开更多
In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary c...In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.展开更多
Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal（oblique）Hermi...Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal（oblique）Hermite matrix are studied further,and thismust be useful for matrix theory and applications（like optimization theory,symplecticgeometry and physics etc）.In the paper,C<sup>m×n</sup>shows m×n compound matrix set,C<sub>n</sub><sup>m×n</sup>shows n step compound invertible matrix set,A<sup>*</sup> shows conjugate transpose matrix of A,展开更多
为了提高重构相干信号测向算法的估计性能,降低算法运算量,提出了一种基于矩阵重构和酉变换方法的酉矩阵重构算法。该算法首先通过酉变换将阵列接收数据从复值计算转换为实值计算,使计算量大大降低;然后计算阵列协方差矩阵并进行特征值...为了提高重构相干信号测向算法的估计性能,降低算法运算量,提出了一种基于矩阵重构和酉变换方法的酉矩阵重构算法。该算法首先通过酉变换将阵列接收数据从复值计算转换为实值计算,使计算量大大降低;然后计算阵列协方差矩阵并进行特征值分解得到信号子空间,再将信号子空间重构为Toeplitz矩阵实现解相干并再次进行酉变换;最后通过特征值分解得到信号子空间并使用最小二乘法实现波达方向(direction of arrival,DOA)估计。相比于改进的旋转不变性的信号参数(estimation of signal parameters via rotational invariance techniques-like,ESPRIT-Like)算法和空间平滑处理算法,由于消除了噪声影响、构造了Toeplitz矩阵以及充分利用了数据的共轭信息,该算法的估计精度更高、具有更高的运算效率且在ESPRIT-Like算法失效的条件下新算法仍能有效估计DOA。本文算法的运行时间是ESPRIT-Like算法的71.2%,实验结果证明了该方法的有效性和真实性。展开更多
A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
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 unifor...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.展开更多
In this paper,we do research on generating unitary matrices for quantum circuits automatically.We consider that quantum circuits are divided into six types,and the unitary operator expressions for each type are offere...In this paper,we do research on generating unitary matrices for quantum circuits automatically.We consider that quantum circuits are divided into six types,and the unitary operator expressions for each type are offered.Based on this,we propose an algorithm for computing the circuit unitary matrices in detail.Then,for quantum logic circuits composed of quantum logic gates,a faster method to compute unitary matrices of quantum circuits with truth table is introduced as a supplement.Finally,we apply the proposed algorithm to different reversible benchmark circuits based on NCT library(including NOT gate,Controlled-NOT gate,Toffoli gate)and generalized Toffoli(GT)library and provide our experimental results.展开更多
After developing the concept of displaced squeezed vacuum states in the non-unitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values in gene...After developing the concept of displaced squeezed vacuum states in the non-unitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values in general form. Then we consider the displacement of the squeezed vacuum states and calculate their photon statistics and their quasiprobabilities. The expectation values of the displaced states are related to the expectation values of the undisplaced states and are calculated for some simplest cases which are sufficient to discuss their categorization as sub-Poissonian and super-Poissonian statistics. A large set of these states do not belong to sub- or to super-Poissonian states but are also not Poissonian states. We illustrate in examples their photon distributions. This shows that the notions of sub- and of super-Poissonian statistics and their use for the definition of nonclassicality of states are problematic. In Appendix A we present the most important relations for SU (1,1) treatment of squeezing and the disentanglement of their operators. Some initial members of sequences of expectation values for squeezed vacuum states are collected in Appendix E.展开更多
A new constellation which is the multiplication of the rotation matrix and the diagonal matrix ac- cording to the number of transmitters is proposed to increase the diversity product, the key property to the performan...A new constellation which is the multiplication of the rotation matrix and the diagonal matrix ac- cording to the number of transmitters is proposed to increase the diversity product, the key property to the performance of the differential unitary space-time modulation. Analyses and the simulation results show that the proposed constellation performs better and 2dB or more coding gain can be achieved over the traditional cyclic constellation.展开更多
Let H∈Cn×n be an n×n unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition H as H=[H11 H12 H21 H22],(0.1) where H11 is its k×k leading principal submatrix; H22 is the c...Let H∈Cn×n be an n×n unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition H as H=[H11 H12 H21 H22],(0.1) where H11 is its k×k leading principal submatrix; H22 is the complementary matrix of H11. In this paper, H is constructed uniquely when its eigenvalues and the eigenvalues of (H|^)11 and (H|^)22 are known. Here (H|^)11 and (H|^)22 are rank-one modifications of H11 and H22 respectively.展开更多
文摘Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.
文摘In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.
基金Supported by the Natural Science Foundation of Chongqing
文摘Along with necessaries applied and the going deeply into the research,that the uni-tary matrix and Hermite matrix are popularized in many kinds,and in this paper uni-versal unitary matrix and universal（oblique）Hermite matrix are studied further,and thismust be useful for matrix theory and applications（like optimization theory,symplecticgeometry and physics etc）.In the paper,C<sup>m×n</sup>shows m×n compound matrix set,C<sub>n</sub><sup>m×n</sup>shows n step compound invertible matrix set,A<sup>*</sup> shows conjugate transpose matrix of A,
文摘为了提高重构相干信号测向算法的估计性能,降低算法运算量,提出了一种基于矩阵重构和酉变换方法的酉矩阵重构算法。该算法首先通过酉变换将阵列接收数据从复值计算转换为实值计算,使计算量大大降低;然后计算阵列协方差矩阵并进行特征值分解得到信号子空间,再将信号子空间重构为Toeplitz矩阵实现解相干并再次进行酉变换;最后通过特征值分解得到信号子空间并使用最小二乘法实现波达方向(direction of arrival,DOA)估计。相比于改进的旋转不变性的信号参数(estimation of signal parameters via rotational invariance techniques-like,ESPRIT-Like)算法和空间平滑处理算法,由于消除了噪声影响、构造了Toeplitz矩阵以及充分利用了数据的共轭信息,该算法的估计精度更高、具有更高的运算效率且在ESPRIT-Like算法失效的条件下新算法仍能有效估计DOA。本文算法的运行时间是ESPRIT-Like算法的71.2%,实验结果证明了该方法的有效性和真实性。
文摘A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
文摘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.
基金This work was funded by the Natural Science Foundation of Jiangsu Province(Grant No:BK20171458)the Yangzhou University International Academic Exchange Fund.
文摘In this paper,we do research on generating unitary matrices for quantum circuits automatically.We consider that quantum circuits are divided into six types,and the unitary operator expressions for each type are offered.Based on this,we propose an algorithm for computing the circuit unitary matrices in detail.Then,for quantum logic circuits composed of quantum logic gates,a faster method to compute unitary matrices of quantum circuits with truth table is introduced as a supplement.Finally,we apply the proposed algorithm to different reversible benchmark circuits based on NCT library(including NOT gate,Controlled-NOT gate,Toffoli gate)and generalized Toffoli(GT)library and provide our experimental results.
文摘After developing the concept of displaced squeezed vacuum states in the non-unitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values in general form. Then we consider the displacement of the squeezed vacuum states and calculate their photon statistics and their quasiprobabilities. The expectation values of the displaced states are related to the expectation values of the undisplaced states and are calculated for some simplest cases which are sufficient to discuss their categorization as sub-Poissonian and super-Poissonian statistics. A large set of these states do not belong to sub- or to super-Poissonian states but are also not Poissonian states. We illustrate in examples their photon distributions. This shows that the notions of sub- and of super-Poissonian statistics and their use for the definition of nonclassicality of states are problematic. In Appendix A we present the most important relations for SU (1,1) treatment of squeezing and the disentanglement of their operators. Some initial members of sequences of expectation values for squeezed vacuum states are collected in Appendix E.
基金Supported by the National Natural Science Foundation of China (No.60402014), and the Doctoral Program Fund of China (No.20010561007).
文摘A new constellation which is the multiplication of the rotation matrix and the diagonal matrix ac- cording to the number of transmitters is proposed to increase the diversity product, the key property to the performance of the differential unitary space-time modulation. Analyses and the simulation results show that the proposed constellation performs better and 2dB or more coding gain can be achieved over the traditional cyclic constellation.
基金This work is supported by the Natural Science Foundation of Fujian Province of China （No. Z0511010）the Natural Science Foundation of China （No. 10571012）.
文摘Let H∈Cn×n be an n×n unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition H as H=[H11 H12 H21 H22],(0.1) where H11 is its k×k leading principal submatrix; H22 is the complementary matrix of H11. In this paper, H is constructed uniquely when its eigenvalues and the eigenvalues of (H|^)11 and (H|^)22 are known. Here (H|^)11 and (H|^)22 are rank-one modifications of H11 and H22 respectively.
