On Entanglement Breaking Channels for Infinite Dimensional Quantum Systems

Максим Евгеньевич Широков

The Schmidt number of a state of an infinite-dimensional composite quantum system is defined and several properties of the corresponding Schmidt classes are considered. It is shown that there are states with given Schmidt number such that any of their countable convex decompositions does not contain pure states of finite Schmidt rank. The classes of infinite-dimensional partially entanglement-breaking channels are considered, and generalizations of several properties of such channels, which were obtained earlier in the finite-dimensional case, are proved. At the same time, it is shown that there are partially entanglement-breaking channels (in particular, entanglement-breaking channels) such that all the operators in any of their Kraus representations are of infinite rank.

Shi‐Dong Liang

Максим Евгеньевич Широков

A definition of the Schmidt number of a state of an infinite dimensional bipartite quantum system is given and properties of the corresponding family of Schmidt classes are considered. The existence of states with a given Schmidt number such that any their countable convex decomposition does not contain pure states with finite Schmidt rank is established. Partially entanglement breaking channels in infinite dimensions are studied. Several properties of these channels well known in finite dimensions are generalized to the infinite dimensional case. At the same time, the existence of partially entanglement breaking channels (in particular, entanglement breaking channels) such that all operators in any their Kraus representations have infinite rank is proved.

Long-Mei Yang, Tao Li, Shao-Ming Fei +1 more

Bui Ngoc Muoi, Nung-Sing Sze

Abstract Entanglement breaking (EB) channels, as completely positive and trace-preserving linear operators, sever the entanglement between the input system and other systems. In the realm of infinite-dimensional systems, a related concept known as strongly EB (SEB) channels emerges. This paper delves into characterizations of SEB channels, delineating sufficient conditions for a channel to be classified as SEB, especially with respect to the commutativity of its range. Moreover, we demonstrate that every closed self-adjoint subspace of trace-zero operators, with the trace norm, is the null space of a SEB channel.

Jinchuan Hou, Wenli Wang