Quantum Information Processing with Continuous Variables and Atomic Ensembles

Quantum information theory promises many advances in science and technology. This thesis presents three different results in quantum information theory.

The first result addresses the theoretical foundations of quantum metrology. It is now well known that quantum-enhanced metrology promises improved sensitivity in parameter estimation over classical measurement procedures. The Heisenberg limit is considered to be the ultimate limit in quantum metrology imposed by the laws of quantum mechanics. It 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 such as the average photon number and the computational resources such as the number of queries that are used in estimation procedures. Here, we reconcile the physical definition of the relevant resources used in parameter estimation 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. Our approach to quantum metrology not only resolves the mentioned paradoxical situations, but also strengths the connection between physics and computer science.

A clear connection between physics and computer science is also present in other results. The second result reveals a close relationship between quantum metrology and the Deutsch-Jozsa algorithm over continuous-variable quantum systems. The Deutsch-Jozsa algorithm, being one of the first quantum algorithms, embodies the remarkable computational capabilities offered by quantum information processing. Here, we develop a general procedure, characterized by two parameters, that unifies parameter estimation and the Deutsch-Jozsa algorithm. Depending on which parameter we keep constant, the procedure implements either the parameter estimation protocol or 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. The entangling protocol requires nearly identical single-photon sources, one ultra-cold ensemble per physical qubit, and regular photo detectors. This procedure is significantly more efficient than any known robust probabilistic entangling operation.