Procrustean entanglement concentration, weak measurements and optimized state preparation for continuous-variable quantum optics

Abstract

In this thesis, we are concerned with continuous-variable quantum optical state engineering protocols. Such protocols are designed to repair or enhance the nonclassical features of a given state. In particular, we build a weak measurement model of Gaussian entanglement concentration of the two mode squeezed vacuum state. This model allows the simultaneous description of all possible ancilla system variations. In addition, it provides an explanation of the Gaussian-preserving property of these protocols while providing a success criterion which links all of the degrees of freedom on the ancilla. Following this, we demonstrate the wider application of weak measurements to quantum optical state engineering by showing that they allow probabilistic noiseless amplifi cation of photon number. We then establish a connection between weak measurements and entanglement concentration as a fundamental result of weak measurements on entangled probes. After this, we explore the trade-off between Gaussian and non-Gaussian operations in the preparation of non-Gaussian pure states. In particular, we suggest that an operational cost for an arbitrary non-Gaussian pure state is the largest Fock state required for its approximate preparation. We consider the extent to which this non-Gaussian operational cost can be reduced by applying unitary Gaussian operations. This method relies on the identification of a minimal core state for any target non-Gaussian pure state.