Infinite Quantum Systems

Yinzhu Wang

The separatability of states in infinite dimensional quantum systems is discussed,some necessary conditions for separable states are presented in infinite dimensional quantum systems,some inequalities are obtained for separable states.These results extend the results of Otfried Guhne(Phys Rev Lett,2004)and Zhang ChengJie(Phys Rev A,2010),which reinforces the exploration of entanglement for states in infinite dimensional quantum systems.

L. E. Reichl

John von Neumann

Re-Bing Wu, Tzyh‐Jong Tarn, Chunwen Li

Manipulation of infinite-dimensional quantum systems is important to controlling complex quantum dynamics with many practical physical and chemical backgrounds. In this paper, a general investigation is casted to the controllability problem of quantum systems evolving on infinite-dimensional manifolds. Recognizing that such problems are related with infinite-dimensional controllability algebras, we introduce an algebraic mathematical framework to describe quantum control systems possessing such controllability algebras. Then we present the concept of smooth controllability on infinite-dimensional manifolds, and draw the main result on approximate strong smooth controllability. This is a nontrivial extension of the existing controllability results based on the analysis over finite-dimensional vector spaces to analysis over infinite-dimensional manifolds. It also opens up many interesting problems for future studies.

Jinchuan Hou

The classical state in tensor product space of considering quantum systems and ancillary quantum systems was constructed.By taking partial trace over ancillary composite quantum systems,the problem of detecting entanglement for states in infinite dimensional bipartite composite quantum system was studied.A necessary and sufficient condition for separable states in infinite dimensional bipartite quantum systems was obtained.The above work extended the relevant results got by Li Nan and Luo Shunlong,and reinforced the exploration of entanglement for states in infinite dimensional quantum systems.