Energy-Constrained Distinguishability Measures for Assessing Performance in Quantum Information Processing

Abstract

The aim of this thesis is to develop a framework for assessing performance in quantum information processing with continuous variables. In particular, we focus on quantifying the fundamental limitations on communication and computation over bosonic Gaussian systems. Due to their infinite-dimensional structure, we make a realistic assumption of energy constraints on the input states of continuous-variable (CV) quantum operations. Our first contribution is to show that energy-constrained distinguishability measures can be used to establish tight upper bounds on the communication capacities of phase-insensitive, bosonic Gaussian channels -- thermal, amplifier, and additive-noise channels. We then prove that an optimal Gaussian input state for the energy-constrained, generalized channel divergence of two particular Gaussian channels is the two-mode squeezed vacuum state that saturates the energy constraint. Next, we develop theoretical and numerical tools based on energy-constrained distinguishability measures to quantify the accuracy in implementing Gaussian unitary operations. Finally, we propose an optimal test for the performance of CV quantum teleportation in terms of the energy-constrained channel fidelity between ideal CV teleportation and its experimental implementation. Here we prove that the optimal state for testing CV teleportation is an entangled superposition of twin-Fock states. These results are relevant for experiments that make use of Gaussian unitaries and CV teleportation.