Transition Phenomena in Networks of Quantum Systems

Abstract

The advances in experimental manipulation and theoretical understanding of single quantum systems has fed the interest in quantum networks: quantum computers, quantum communication networks and multimode interferometers. According to statistical physics, a set of probabilistically behaving individual systems can exhibit critical behaviour when connected. In this paper we show that transition phenomena exist also in networks which behave probabilistically not because of finite temperature but due to their quantum nature1. We define a model which carries in its structure a formal analogy to the two-dimensional Ising-model. Such networks can be experimentally realized by various active (non-unitary) and passive (unitary) components. We give physical meaning to the transitions found. In the case of active components, such as amplifiers, the transition point coincides with the fundamental cloning limit given by quantum mechanics. We indicate how the transition phenomena could be observed, and discuss their significance and connection to quantum information related issues such as quantum computation and quantum cellular automata.KeywordsTransition PointCellular AutomatonIsing ModelQuantum ComputerQuantum NetworkThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.