Separability of Quantum Systems: A Density Matrix Approach

Ming Li, Wang Jing

Romàn R. Zapatrin

For a given density matrix $ρ$ of a bipartite quantum system an asymptotical separability criterion is suggested. Using the continuous ensemble method, a sequence of separable density matrices is built which converges to $ρ$ if and only if $ρ$ is separable. The convergence speed is evaluated and for any given tolerance parameter $κ$ an iterative procedure is suggested which decides in finite number of steps if there exists a separable density matrix $ρ_κ$ which differs from the matrix $ρ$ by at most $κ$.

Cao Huai-xin

In this note,we give a representation of density matrix for a bipartite quantum system and a neces-sary condition for separability of density matrix of mixed states in a bipartite quantum system of arbitrary dimen-tion.We show that if density matrix of mixed states in a bipartite quantum system of arbitrary dimension is separa-ble,then the trace norm of constructive matrix is less than or equal to 1.

Chi‐Shan Yu, H. S. Song

F. Selleri

Chao Zhao, Qizhi Guo, Weihan Tan

The “separability problem” in quantum information theory is a quite important and well-known hard problem. The low-dimensional system satisfies the PPT criterion. However, the high-dimensional system problem has been shown to be NP-hard problem. In general, it is very difficult to find the analytic solution of the density matrix for the high-dimensional system. Therefore, getting an analytic solution for two-qubit system is an interesting and useful problem. We propose a novel criterion for separability and entanglement-verification of two-qubit system. We expressed the density matrix by a sum of a principal density matrix and six separable density matrices. The necessary and sufficient conditions for the two-qubit system include that if the four involved coefficients [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and the principal density matrix [Formula: see text] are separable, then the two-qubit system is separable, otherwise the two-qubit system is entangled. Finally, our criterion results in a totally different conclusion compared to Horodecki’s criterion. We believe that the new criterion is more stringent than existing PPT methods.