Quantum Complexities and Quantum Interfaces

I propose a research project within the field of Quantum Information. The project is divided into two main lines of research. The first is abstract and addresses fundamental questions concerning the quantum computational complexity and the complexity of describing quantum states. The second is physically motivated and deals with the realization of quantum information processors. The fundamental problem of how difficult it is to describe a classical bit string has been investigated by A. N. Kolmogorov. The notion of Kolmogorov complexity led to great success in Classical Information, as it can be used as a general proof method for a variety of problems. The quantum counterpart, that is the number of classical bits required to describe a quantum state, has recently attracted interest and several definitions of the quantum Kolmogorov complexity have been presented. The first goal will be to clarify the connection between these definitions and to apply them to several physical situations. Further, the quantum Kolmogorov complexity will be related to the quantum computational complexity. A certain class of quantum algorithms will be investigated with the aim to single out the main quantum--mechanical features that allow one to perform certain computations quantum--mechanically faster than classically possible. In the second part of the project, both, new systems and the integration of different systems will be analyzed with respect to their suitability for quantum informational tasks, like quantum computation and quantum communication. In particular, a novel scheme, based on a quantum interface between quantum optical and solid state systems, will be investigated. One of the considered systems is composed of ensembles of polar molecules and Cooper pair boxes. The realization of quantum gates using those systems will be studied. Furthermore, the possibility to store and read out Quantum Information, as well as the effects of decoherence in those systems will be investigated. The entanglement within the molecular ensemble as well as the entanglement between the ensemble and the Cooper pair box will be qualified and quantified.