Quantum state transfer between cells and binary tree model

María Luisa Dalla Chiara, Roberto Giuntini, Alberto Leporati +1 more

Tommaso Tufarelli, Vittorio Giovannetti

Quantum state propagation over binary-tree configurations is studied in the context of quantum spin networks. For a binary tree of order 2, a simple protocol is presented which allows one to achieve arbitrary high transfer fidelity. It does not require fine-tuning of local fields and two-node coupling of the intermediate spins. Instead it assumes simple local operations on the intended receiving node: their role is to brake the transverse symmetry of the network that induces an effective refocusing of the propagating signals. Some ideas on how to scale up these effects to a binary tree of arbitrary order are discussed.

Naghi Behzadi, Bahram Ahansaz

Luís Tarrataca, Andreas Wichert

Peter J. Love

Vincent Pouthier, Lucie Pepe, Saad Yalouz

In this work, the dynamics of a quantum walker on glued trees is revisited to understand the influence of the architecture of the graph on the efficiency of the transfer between the two roots. Instead of considering regular binary trees, we focus our attention on leafier structures where each parent node could give rise to a larger number of children. Through extensive numerical simulations, we uncover a significant dependence of the transfer on the underlying graph architecture, particularly influenced by the branching rate (M) relative to the root degree (N). Our study reveals that the behavior of the walker is isomorphic to that of a particle moving on a finite-size chain. This chain exhibits defects that originate in the specific nature of both the roots and the leaves. Therefore, the energy spectrum of the chain showcases rich features, which lead to diverse regimes for the quantum-state transfer. Notably, the formation of quasi-degenerate localized states due to significant disparities between M and N triggers a localization process on the roots. Through analytical development, we demonstrate that these states play a crucial role in facilitating almost perfect quantum beats between the roots, thereby enhancing the transfer efficiency. Our findings offer valuable insights into the mechanisms governing quantum-state transfer on trees, with potential applications for the transfer of quantum information.