Topics on quantum entanglement: anti-Unruh phenomena and holographic quantum energy teleportation

Abstract

無中文摘要Two topics on entanglement are concerned in this thesis: One is the decoherence patterns of a topological qubit made of two Majorana zero modes in the generic linear and circular motions and the other is a simplified protocol of quantum energy teleportation (QET) for the holographic conformal field theory in three-dimensional anti-de Sitter space with or without a black hole. On the first topic, the exact reduced dynamics without Markov approximation is shown. For general time scale, the acceleration causes thermalization as expected by Unruh effect. However, for the short-time scale, the rate of decoherence is anti-correlated with the acceleration, as a kind of decoherence impedance. This is in fact related to the “anti-Unruh" phenomenon previously found by studying the transition probability of Unruh-DeWitt detector. Besides, the information backflow is observed by some time modulations of coupling constant or acceleration. Moreover, it also shows that some incoherent accelerations of the constituent Majorana zero modes can preserve the coherence instead of thermalizing it. On the second topic, as a tentative proposal, the standard QET is simplified by replacing Alice’s local measurement with the local projection. At the same time, Bob’s local operation of the usual QET for extracting energy is mimicked by deforming the UV surface with a local bump. Adopting the surface-state duality, this deformation corresponds to local unitary. In this protocol, the extraction energy is always positive. Moreover, the ratio of extraction energy to the injection one is an universal function of the UV surface deformation profile.