Entanglement of Indistinguishable Particles: Second Quantization Approach

Abstract

Quantum entanglement is a key resource for numerous quantum information tasks, quantum computing, quantum sensing and related quantum technologies. However, the generation, detection and quanti cation of entanglement may be quite complicated depending on the nature and properties of the pertaining system. In this thesis, we study various methods for detection and quanti cation as resource theory of entanglement for a system of particles in the context of indistinguishability transition of particles' identity. We start our discussion with the system of distinguishable particles and discuss di erent methods of entanglement detection and quanti cation such as Schmidt decomposition and von Neumann Entropy, with all their merits and demerits. The notion of entanglement is extended for the quantum systems composed of indistinguishable particles and, its detection and quanti cation is analyzed. It is found that the conventional Schmidt decomposition deeds to be modi ed, in the form of Slater- Schmidt decomposition, when the particles' identity becomes indistinguishable. In order to build a comprehensive analysis, we review various techniques to make a global entanglement detection scheme, such as, so-called no label approach which becomes complicated in the case of indistinguishable particles. Finally, we discuss the second quantization approach which helps to reduce the complications of symmetrization postulate for indistinguishable particles and suggest a way to develop a uni ed approach to all quantum systems.