arXiv subjects
Publications and source records attributed to Xiaofen Huang.
We study the uncertainty relation in the product form of variances and obtain some new uncertainty relations with weight, which are shown to be tighter than those derived from the Cauchy Schwarz inequality.
We study the trade-off relations given by the l_1-norm coherence of general multipartite states. Explicit trade-off inequalities are derived with lower bounds given by the coherence of either bipartite or multipartite reduced density matrices. In particular, for pure three-qubit states, it is explicitly shown that the trade-off inequality is lower bounded by the three tangle of quantum entanglement.
We study the stochastic local operation and classical communication (SLOCC) equivalence for arbitrary dimensional multipartite quantum states. For multipartite pure states, we present a necessary and sufficient criterion in terms of their coefficient matrices. This condition can be used to classify some SLOCC equivalent quantum states with coefficient matrices having the same rank. For multipartite mixed state, we provide a necessary and sufficient condition by means of the realignment of matrix. Some detailed examples are given to identify the SLOCC equivalence of multipartite quantum states.
We study the fully entangled fraction of a quantum state. An upper bound is obtained for arbitrary bipartite system. This upper bound only depends on the Frobenius norm of the state.
We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of $n\times n$ bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable pure state decompositions of these states are explicitly constructed when they are PPT.
We give an exact solution to the nonlinear optimization problem of approximating a Hermitian matrix by positive semi-definite matrices. Our algorithm was then used to judge whether a quantum state is entangled or not. We show that the exact approximation of a density matrices by tensor product of positive semi-definite operators is determined by the additivity property of the density matrix.
We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show that a density operator is separable if and only if the separable indicator is non-negative. We then derive two bounds for the separable indicator in terms of the spectrum of the factor operators in the tensor summands.