A Loss Resilient Entanglement Swapping Protocol using Non-Classical States of Light

Distributing and sharing entanglement at a distance is a key ingredient in many future quantum communication protocols, however entanglement is a fragile resource and can break down upon interacting with the environment. Within this thesis we present two possible entanglement swapping protocols, and show that these protocols are resilient to small levels of photonic losses. We propose the use of these protocols in quantum communication schemes that require shared entangled qubits, in the form of a Bell state.
The input states to our proposed protocols are hybrid entangled states, which are discrete-variable and continuous-variable entangled states. We use the vacuum and
single photon Fock state as our discrete half, which is stationary in our entanglement swapping protocol, whereas the continuous variable half is modelled as travelling through lossy optical fibre before being measured. The first protocol uses coherent states in a superposition as propagating modes in our entanglement swapping setup,
whereas the second, more complicated, protocol uses superposed cat states.
We model photonic losses by applying a beam-splitter of transmission T to our propagating continuous variable modes, along with an input vacuum state. We also model the more realistic circumstance in which the losses in these two continuous variable modes are not equal. We then detect these continuous variable modes using a vacuum projective measurement and balanced homodyne detection. We also investigate homodyne measurement imperfections and non-ideal outcomes, as well as success probabilities of these measurement schemes. We calculate the entanglement negativity and linear entropy of our final two qubit state, as well as fidelity against the |\Phi^+> Bell state in the coherent state protocol, and a phase-rotated |\Phi^+(\alpha)> Bell state in the cat state regime.
We demonstrate that a small amount of loss mismatch does not destroy the overall entanglement, thus demonstrating the physical practicality of this protocol.