In this paper,we study some inclusion sets of US-eigenvalues and U-eigenvalues based on quantum information.We give three inclusion sets theorems of US-eigenvalues and two inclusion sets theorems of U-eigenvalues.And ...In this paper,we study some inclusion sets of US-eigenvalues and U-eigenvalues based on quantum information.We give three inclusion sets theorems of US-eigenvalues and two inclusion sets theorems of U-eigenvalues.And we obtain the relationships among these inclusion sets.Some numerical examples are shown to illustrate the conclusions.展开更多
The problem of computing geometric measure of quantum entanglement for symmetric pure states can be regarded as the problem of finding the largest unitary symmetric eigenvalue(US-eigenvalue)for symmetric complex tenso...The problem of computing geometric measure of quantum entanglement for symmetric pure states can be regarded as the problem of finding the largest unitary symmetric eigenvalue(US-eigenvalue)for symmetric complex tensors,which can be taken as a multilinear optimization problem in complex number field.In this paper,we convert the problem of computing the geometric measure of entanglement for symmetric pure states to a real polynomial optimization problem.Then we use Jacobian semidefinite relaxation method to solve it.Some numerical examples are presented.展开更多
基金supported in part by the National Natural Science Foundation of China(No.12071097)the Joint Guidance Natural Science Foundation of Heilongjiang Province of China(No.LH2021A004)the Basic Scientific Research Foundation of National Defense(No.JCKYS2021604SSJS002)
文摘In this paper,we study some inclusion sets of US-eigenvalues and U-eigenvalues based on quantum information.We give three inclusion sets theorems of US-eigenvalues and two inclusion sets theorems of U-eigenvalues.And we obtain the relationships among these inclusion sets.Some numerical examples are shown to illustrate the conclusions.
基金the Research Programme of National University of Defense Technology(No.ZK16-03-45).
文摘The problem of computing geometric measure of quantum entanglement for symmetric pure states can be regarded as the problem of finding the largest unitary symmetric eigenvalue(US-eigenvalue)for symmetric complex tensors,which can be taken as a multilinear optimization problem in complex number field.In this paper,we convert the problem of computing the geometric measure of entanglement for symmetric pure states to a real polynomial optimization problem.Then we use Jacobian semidefinite relaxation method to solve it.Some numerical examples are presented.
