Controlling the Shannon Entropy of Quantum Systems

Abstract

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

On Reachable and Controllability Sets for Minimum-Time Control of an Open Two-Level Quantum System

“…Reference [49] considers an open four-level atomic system and analyzes coherent control for the von Neumann entropy (total and reduced versions) via quantum interference. In [50][51][52], a controller design approach for a closed quantum system described by the Scrödinger equation in terms of the von Neumann/Shannon entropy was proposed. Reference [53] considers the spatial control of entropy for a three-level ladder-type atomic system that interacts with optical laser fields and an incoherent pumping field.…”

Continuous Controller Design for Quantum Shannon Entropy

“…For pure state in closed quantum systems, our previous work [12] proposed the discretized controller design method for Shannon entropy. This paper proposes the continuous Shannon entropy controller, which can achieve quite accurate control effect.…”

Química de la información: aspectos clásicos y cuánticos de fenómenos moleculares

“…Para nalizar es importante mencionar que la teor a de control de sistemas cu anticos y la qu mica ultrafr a son campos que tambi en pueden encontrar interesante este tipo de aplicaciones en las que se genera un nuevo estado a partir de uno anterior que puede actuar como una especie de dato de entrada. En trabajos recientes se ha conjeturado que manipular la densidad electr onica es posible a trav es de modi car la entrop a de Shannon [264,265], lo cual se puede generalizar a trav es de los resultados obtenidos en este estudio; es decir la densidad electr onica, en principio, se puede manipular a trav es de cambiar su contenido informacional. Si este conocimiento lo llevamos a la qu mica ultrafr a, donde recientemente se ha demostrado que es posible manipular los estados vibracionales y rotacionales en reacciones qu micas [195], entonces estar amos m as cerca de generar estados determinados en una reacci on qu mica, tal como el estado de m aximo entrelazamiento.…”