On the locality of indistinguishable quantum systems

Thesis

This thesis investigates local realism in quantum indistinguishable particle systems, focusing on bosonic, fermionic, and 2D non-abelian anyonic systems. The local realism of quantum indistinguishable particle systems is asserted. It proves annihilation operators represent the local ontic states in these systems. It closes the literature gap on obtaining Deutsch-Hayden descriptors in indistinguishable particle systems. The prima facie paradox of action at a distance using fermionic annihilation operators as descriptors is resolved. The work provides examples of using and interpreting the annihilation operators as local ontic states. It contains the novel construction and characterisation of the annihilation operators for 2 D non-abelian anyonic systems. The explicit form of Fibonacci anyon annihilation operators is provided, and their usefulness is shown in expressing the anyonic Hubbard model Hamiltonian algebraically. By studying the indistinguishable particle systems’ local realistic structure, the thesis showcases the relevance of the choice of subsystem lattice and exotic possible compositions of subsystems.

Authors: Tibau Vidal, N

• DOI: 10.5287/ora-gadxmg4z9
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: fermions; anyons; local realism; ontic states
• Subjects: Quantum theory