Quantum Information Processing with Continuous Variables and Atomic Ensembles

TL;DR

This thesis advances quantum information theory by establishing a universal Heisenberg limit, linking quantum metrology with the Deutsch-Jozsa algorithm in continuous variables, and proposing an efficient method for generating cluster states using atomic ensembles.

Contribution

It introduces a universal Heisenberg limit, unifies parameter estimation with the Deutsch-Jozsa algorithm, and presents a novel, efficient scheme for creating cluster states with atomic ensembles.

Findings

Established a novel ultimate Heisenberg limit for quantum measurements.

Unified parameter estimation and Deutsch-Jozsa algorithm in continuous-variable systems.

Proposed an efficient scheme for generating cluster states using atomic ensembles and dipole blockade.

Abstract

This thesis presents three different results in quantum information theory. The first result addresses the theoretical foundations of quantum metrology. The Heisenberg limit considered as the ultimate limit in quantum metrology sets a lower bound on how precisely a physical quantity can be measured given a certain amount of resources in any possible measurement. Recently, however, several measurement procedures have been proposed in which the Heisenberg limit seemed to be surpassed. This led to an extensive debate over the question how the sensitivity scales with the physical resources and the computational resources that are used in estimation procedures. Here, we reconcile the physical definition of the relevant resources with the information-theoretical scaling in terms of the query complexity of a quantum network. This leads to a novel and ultimate Heisenberg limit that applies to all conceivable measurement procedures. The second result reveals a close relationship between quantum metrology and the Deutsch-Jozsa algorithm over continuous-variable quantum systems. Here, we develop a general procedure, characterized by two parameters, that unifies parameter estimation and the Deutsch-Jozsa algorithm. The procedure estimates a value of an unknown parameter with Heisenberg-limited precision or solves the Deutsch-Jozsa problem in a single run without the use of any entanglement. The third result illustrates how physical principles that govern interaction of light and matter can be efficiently employed to create a computational resource for a (one-way) quantum computer. More specifically, we demonstrate theoretically a scheme based on atomic ensembles and the dipole blockade mechanism for generation of the so-called cluster states in a single step. This procedure is significantly more efficient than any known robust probabilistic entangling operation.