Universality in Dynamical Formation of Entanglement for Quantum Chaos

At the dawn of the quantum mechanics, entangled states of spatially separated bi-particle systems triggered fierce discussions because of their paradoxical property [1]. These discussions lead to the finding of the inequalities which measure how quantum systems deviate from the classical reality [2]. Recently, a renewed interest has been paid to entanglement since it is recognized as an invaluable resource in quantum computation and quantum communication [3]. Thus, the information theory and the circuit theory for entangled qubits has become fast growing fields. On the other hand, in the quantum theory of open systems, dynamical formation of entanglement between a system and its environment is a target of the research. In these studies, it is supposed that uncontrolled formation of entanglement causes the loss of quantum coherence in the system and leads to the appearance of the classical reality. Then, the loss of quantum coherence is considered to provide the foundation of the statistical physics [4, 5]. Also in the quantum computation, dynamical formation of entanglement between qubits and their environment is a crucial subject since it can give rise to erroneous operations of quantum computers. In the traditional study on the dynamical formation of entanglement, the system is supposed to interact with an environment composed of a large number of degrees of freedom. Then, the interaction with the environment causes complicated uncontrollable formation of entanglement, leading to the loss of coherence in the system. However, interaction with an environment is not the only cause of complicated processes of forming entanglement. Actually, dynamical formation of entanglement by quantum chaos has been an active topic these days