Quantum correlations in and beyond quantum entanglement in bipartite continuous variable systems

Abstract

This thesis explores the role of non-classical correlations in bipartite continuous variable quantum systems, and the approach taken is three-fold. We show that given two initially entangled atomic ensembles, it is possible to probabilistically increase the entanglement between them using a beamsplitter-like interaction formed from two quantum non-demolition (QND) interactions with auxiliary polarised light modes. We then develop an elegant method to calculate density matrix elements of non-Gaussian bipartite quantum states and use this to show that the entanglement in a two mode squeezed vacuum can be distilled using QND interactions and non-Gaussian elements. Secondly, we introduce a potential new measure of quantum entanglement in bipartite Gaussian states. This measure has an operational meaning in quantum cryptography and provides an upper bound on the amount of a secret key that can be distilled from a Gaussian probability distribution shared by two conspirators, Alice and Bob, given the presence of an eavesdropper, Eve. Finally, we go beyond the realm of quantum entanglement to explore other non-classical correlations in continuous variable systems. We provide solutions for a number of these measures on two mode Gaussian states and introduce the Gaussian Ameliorated Measurement Induced Disturbance (GAMID). The interplay between these different measures and quantum entanglement is examined. We then attempt to take small steps into the non-Gaussian regime by computing these non-classicality measures on the three-parameter continuous variable Werner states.