Quantum Information Processing and Quantum Communications

Quantum Cellular automata, Random walks, and Turing machines

aula 102 - Martedì 1 giugno ore 15.00
  REINHARDT WERNER, Technical University of Braunschweig

Professor at the Technical University of Braunschweig, is the leader of a research group on quantum information theory. He studied in Marburg, in the group of G. Ludwig, and has been working on the conceptual and mathematical foundations of quantum theory, including quantum statistical mechanics. He is expecially known among physicists of Quantum Information for his studies on quantum cloning, capacities of channels, quantum error correction, and entanglement. Author of popular reviews
of Quantum Information.

Reinhardt Werner
  The notion of quantum cellular automata is expressed most naturally in the language of observable algebras. We present a general theory, allowing a decomposition of arbitrary quantum cellular automata into two steps of unitary transformations acting on local blocks. General construction methods are presented, including the quantization of reversible classical cellular automata, and the second quantization of random walks. Quantum random walks (see e.g., the recent review of J. Kempe) are shown to be special cases of quantum cellular automata, restricted to a subspace of configurations withonly one particle present. Similarly, quantum turing machines are shown to be special cellular automata, proving that quantum cellular automata are capable of universal quantum computation.