Theoretical investigations of separability and entanglement of bipartite quantum systems

Hendra I. Nurdin, Ian R. Petersen, M. R. James

This technical note uses a system theoretic approach to show that classical linear time invariant controllers cannot generate steady state entanglement in a bipartite Gaussian quantum system which is initialized in a Gaussian state. The technical note also shows that the use of classical linear controllers cannot generate entanglement in a finite time from a bipartite system initialized in a separable Gaussian state. The approach reveals connections between system theoretic concepts and the well known physical principle that local operations and classical communications cannot generate entangled states starting from separable states.

Ved Prakash Gupta, Prabha Mandayam, Viakalathur Shankar Sunder

Aldo Moro, Settore Scientifico, Disciplinare Fis +1 more

Yao-Min Di

Entanglement for a three-parameter class of states in bipartite quantum system is investigated.The concurrence for these states in 2n quantum system is calculated and their lower bound of the entanglement of formation is discussed.The negativity for these states in mn(2≤m≤n) quantum system is calculated and the analytic expressions are obtained.Investigation reveals that for θ=π/4,entanglement of the states reaches its maximum,and the states come down to the two-parameter class of states researched by some authors.For these three-parameter states in 2n quantum system,all PPT states are separable,and all NPT states are entangled.But for higher dimensional three-parameter states,the similar conclusion does not exist.

Fabio Benatti

Chengwang Niu, Guofu Xu, Longjiang Liu +3 more

It is known that an interacting bipartite system evolves as an entangled state in general, even if it is initially in a separable state. Due to the entanglement of the state, the geometric phase of the system is not equal to the sum of the geometric phases of its two subsystems. However, there may exist a set of states in which the nonlocal interaction does not affect the separability of the states, and the geometric phase of the bipartite system is then always equal to the sum of the geometric phases of its subsystems. In this article, we illustrate this point by investigating a well-known physical model. We give a necessary and sufficient condition in which a separable state remains separable so that the geometric phase of the system is always equal to the sum of the geometric phases of its subsystems.