Boundary dynamics driven entanglement

Abstract

We will show how it is possible to generate entangled states out of unentangled ones on a bipartite system by means of dynamical boundary conditions. The auxiliary system is defined by a symmetric but not self-adjoint Hamiltonian and the space of self-adjoint extensions of the bipartite system is studied. It is shown that only a small set of them leads to separable dynamics and they are characterized. Various simple examples illustrating this phenomenon are discussed, in particular we will analyze the hybrid system consisting of a planar quantum rotor and a spin system under a wide class of boundary conditions.

The topology and geometry of self-adjoint and elliptic boundary conditions for Dirac and Laplace operators

“…There are many other physical phenomena involving the 'boundary' of physical systems that it would be simply impossible to enumerate here. We would just like to mention a few recent contributions related to different physical problems: the analysis of boundary conditions and the Casimir effect in [As06], [As07], the role of boundary conditions in topological insulators [As13], and boundary conditions generated entanglement [Ib14b].…”

On the theory of self-adjoint extensions of symmetric operators and its applications to quantum physics

“…A more general theorem that can be found in [IMPP12,Theorem 2] shows that separable dynamics can be achieved if and only if the boundary conditions are of the form U = U A ⊗ I .…”

“…Since the aim of these lectures is to introduce the topics to a wide audience we will skip the most technical details. Most of them can be found in [IMPP12].…”

Quantum Control at the Boundary

“…The QCB paradigm has been used to show how to generate entangled states in composite systems by suitable modifications of the boundary conditions [30]. The relation of QCB and topology change has been explored in [39] and recently used to describe the physical properties of systems with moving walls ( [18], [19], [16], [17], [21]), but in spite of its intrinsic interest some basic issues such as the QCB controllability of simple systems has never been addressed.…”