Generic Quantum Systems

Philipp O. J. Scherer

Jarosław K. Korbicz, Edgar A. Aguilar, Piotr Ćwikliński +1 more

Measurement is of central interest in quantum mechanics as it provides the link between the quantum world and the world of everyday experience. One of the features of everyday experience is its robust, objective character, contrasting the delicate nature of quantum systems. Here we analyze in a completely model-independent way the celebrated von Neumann measurement process, using recent techniques of information flow, studied in open quantum systems. We show the generic appearance of objective results in quantum measurements, provided we macroscopically coarse-grain the measuring apparatus and wait long enough. To study genericity, we employ the widely used Gaussian unitary ensemble of random matrices and the Hoeffding inequality. We derive generic objectivization time scales, given solely by the interaction strength and the systems' dimensions. Our results are manifestly universal and are a generic property of von Neumann measurements.

Wonmin Son, Jinhyoung Lee, M. S. Kim

We present generic Bell inequalities for multipartite multi-dimensional systems. The inequalities that any local realistic theories must obey are violated by quantum mechanics for even-dimensional multipartite systems. A large set of variants are shown to naturally emerge from the generic Bell inequalities. We discuss particular variants of Bell inequalities, that are violated for all the systems including odd-dimensional systems.

Toshiya Takami, Hiroshi Fujisaki

The rotating-wave approximation and its validity in multi-state quantum systems are studied through analytic approaches. Their applicability is also verified from the viewpoint of generic states by the use of direct numerical integrations of the Schrödinger equation. First, we introduce an extension of the rotating-wave approximation for multi-state systems. Under an assumption that a smooth transition is induced by the optimal field, we obtain three types of analytic control fields to demonstrate their validity and deficiency for generic systems represented by random matrices. Through the comparison, we conclude that the analytic field based on our coarse-grained approach outperforms the other ones for generic quantum systems with a large number of states. Finally, the further extension of the analytic field is introduced for realistic chaotic systems and its validity is shown in banded random matrix systems.

Philipp O. J. Scherer