Entanglement Between Noncomplementary Parts of Many-Body Systems

This thesis investigates the structure and behaviour of entanglement, the purely quantum mechanical part of correlations, in many-body systems, employing both numerical and analytical techniques at the interface of condensed matter theory and quantum information theory. Entanglement can be seen as a precious resource which, for example, enables the noiseless and instant transmission of quantum information, provided the communicating parties share a sufficient “amount” of it. Furthermore, measures of entanglement of a quantum mechanical state are perceived as useful probes of collective properties of many-body systems. For instance, certain measures are capable of detecting and classifying ground-state phases and, particularly, transition (or critical) points separating such phases. Chapters 2 and 3 focus on entanglement in many-body systems and its use as a potential resource for communication protocols. They address the questions of how a substantial amount of entanglement can be established between distant subsystems, and how efficiently this entanglement could be “harvested” by way of measurements. The subsequent chapters 4 and 5 are devoted to universality of entanglement between large collections of particles undergoing a quantum phase transition, where, despite the enormous complexity of these systems, collective properties including entanglement no longer depend crucially on the microscopic details.

Table of Contents

1 Introduction

2 Exploit ing Quench Dynamics in Spin Chains for Distant Entang lement and Quantum Communication

3 Extraction of Pure Entangled States From Many-Body Systems by Distant Local Projections

4 Scaling of Negativity Between Separated Blocks in Spin Chains at Criticality

5 Universality of the Negativity in the Lipkin–Meshkov–Glick Model

6 Conclusio ns and Out look

Review

From the reviews:

“The theses brings new and very interesting knowledge on the quantum information field. … this thesis gives a new insight of entanglement between noncomplementary regious of many-body systems, with interesting discussions and well carried out mathematical models.” (Nicolae Constantinescu, Zentralblatt MATH, Vol. 1222, 2011)