Separability

Li Hua

Separable operators and PPT operators on a finite dimensional tensor product space are introduced.Then,general forms of separable self-adjoint operators,separable projective operators and separable positive operators are obtained.The relationship between separable operators and PPT operators are proved,and some examples which are PPT operators but not separable operators are given.Lastly,separable maps and PPT maps are introduced and discussed,and it is proved that every separable map maps a PPT operator as a PPT operator.

Shengjun Wu, J. Anandan

S N Filippov, K Yu Magadov, Maria Anastasia Jivulescu

Absolutely separable states ϱ remain separable under arbitrary unitary transformations . By example of a three qubit system we show that in a multipartite scenario neither full separability implies bipartite absolute separability nor the reverse statement holds. The main goal of the paper is to analyze quantum maps resulting in absolutely separable output states. Such absolutely separating maps affect the states in a way, when no Hamiltonian dynamics can make them entangled afterwards. We study the general properties of absolutely separating maps and channels with respect to bipartitions and multipartitions and show that absolutely separating maps are not necessarily entanglement breaking. We examine the stability of absolutely separating maps under a tensor product and show that is absolutely separating for any N if and only if Φ is the tracing map. Particular results are obtained for families of local unital multiqubit channels, global generalized Pauli channels, and combination of identity, transposition, and tracing maps acting on states of arbitrary dimension. We also study the interplay between local and global noise components in absolutely separating bipartite depolarizing maps and discuss the input states with high resistance to absolute separability.

Shengjun Wu, J. Anandan

A quantum state which can be written as a convex sum of product states is a separable state; such a convex sum allows for a local description. There are many different local descriptions for a given separable state, and some new results about the minimal number of product states in the convex sum wil be given in this paper. Any quantum state is either entangled or separable. However it is very difficult to tell whether a given state is separable or entangled. This difficulty has not been solved yet although a lot of separability criteria have already be proposed. The various separability criteria will also be discussed.

Bernard d’Espagnat