Aspects of Quantum Entanglement and Indistinguishability

Abstract: This thesis investigates the entanglement of distinguishable and indistinguishable particles, introducing a new error model for Hardy's test, experimentally verified using superconducting qubits. We address challenges in implementing quantum protocols based on this test and propose potential solutions and present two performance measures for qubits in superconducting quantum computers. We demonstrate that if quantum particles can create hyper-hybrid entangled states and achieve unit fidelity quantum teleportation, arbitrary state cloning is possible. This leads to two no-go theorems: hyper-hybrid entangled states cannot be formed with distinguishable particles, and unit fidelity quantum teleportation is unattainable with indistinguishable particles. These results establish unique correlations for each particle type, creating a clear distinction between the two domains. We also show that hyper-hybrid entangled states can be formed with indistinguishable fermions and generalize this for both fermions and bosons. We develop a generalized DoF trace-out rule applicable to single or multiple degrees of freedom for both types of particles. This framework allows us to derive expressions for teleportation fidelity and singlet fraction, establishing an upper bound for the generalized singlet fraction. We present an optical circuit that generates entanglement in distinguishable particles. Using our trace-out rule, we show that for two indistinguishable particles with multiple DoFs, the monogamy of entanglement can be maximally violated. We assert that indistinguishability is essential for this violation in qubit systems. For three indistinguishable particles, we confirm that monogamy is upheld using squared concurrence. Finally, we propose a novel entanglement swapping protocol involving two indistinguishable particles, enhancing quantum networks and quantum repeaters.