We investigate separability of mixed states in bipartite and multipartite quantum systems. If a quantum state in a bipartite system of arbitrary dimension (or in 2 × 2 × N quantum systems) is separable, we s...We investigate separability of mixed states in bipartite and multipartite quantum systems. If a quantum state in a bipartite system of arbitrary dimension (or in 2 × 2 × N quantum systems) is separable, we show that some quantity in relationto Hermitian matrix is positive.展开更多
In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz ...In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.展开更多
The general expression with the physical significance and positive-definite condition of the eigenvalues of 4 × 4 Hermitian and trace-one matrix are obtained. The obvious expression of Peres' separability con...The general expression with the physical significance and positive-definite condition of the eigenvalues of 4 × 4 Hermitian and trace-one matrix are obtained. The obvious expression of Peres' separability condition for an arbitrary state of two qubits is then given and its operational feature is enhanced. Furthermore, we discuss some applications to the calculation of the entanglement, the upper bound of the entanglement, and a model of the transfer of entanglement in a qubit chain with noise.展开更多
Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices w...Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.展开更多
文摘We investigate separability of mixed states in bipartite and multipartite quantum systems. If a quantum state in a bipartite system of arbitrary dimension (or in 2 × 2 × N quantum systems) is separable, we show that some quantity in relationto Hermitian matrix is positive.
文摘In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.
文摘The general expression with the physical significance and positive-definite condition of the eigenvalues of 4 × 4 Hermitian and trace-one matrix are obtained. The obvious expression of Peres' separability condition for an arbitrary state of two qubits is then given and its operational feature is enhanced. Furthermore, we discuss some applications to the calculation of the entanglement, the upper bound of the entanglement, and a model of the transfer of entanglement in a qubit chain with noise.
文摘Let Q be the quaternion division algebra over real field F, Denote by Hn（Q） the set of all n x n hermitian matrices over Q. We characterize the additive maps from Hn（Q） into Hm（Q） that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn （QR） into Hm （QR） that preserve rank-1 matrices are also given.
