Visualizing Entanglement in multi-Qubit Systems

In the field of quantum information science and technology, the representation and visualization of quantum states and related processes are essential for both research and education. In this context, a focus especially lies on ensembles of few qubits. There exist many powerful representations for single-qubit and multi-qubit systems, such as the famous Bloch sphere and generalizations. Here, we utilize the dimensional circle notation as a representation of such ensembles, adapting the so-called circle notation of qubits and the idea of representing the n-particle system in an n-dimensional space. We show that the mathematical conditions for separability lead to symmetry conditions of the quantum state visualized, offering a new perspective on entanglement in few-qubit systems and therefore on various quantum algorithms. In this way, dimensional notations promise significant potential for conveying nontrivial quantum entanglement properties and processes in few-qubit systems to a broader audience, and could enhance understanding of these concepts as a bridge between intuitive quantum insight and formal mathematical descriptions.Comment: 22 pages, 20 figure

Electrochromic graduated filters with symmetric electrode configuration

Graduated optical filters are commonly used for spatial image control as they are capable of darkening the overexposed parts of the image specifically. However, they lack flexibility because each filter has a fixed transmission distribution. We herein present a fully controllable graduated filter based on the electrochromic device. Its graduated transmission distribution can be spatially controlled by the application of multiple electric potentials. In this way, the control of the gradient’s position and its width, transmission and angular orientation is possible. Simulation of both the spatial potential distribution and the resultant optical absorption distribution are conducted to optimize the electrode configuration and furthermore to derive a control dataset that facilitates the adjustment and thus the application of the graduated filter. Based on three objective and quantitative criteria, we identify the electrode configuration with the highest flexibility in all four controls, manufacture the device using a gravure printing process for the nanoparticle electrodes and show its successful application

Electrochromic graduated filters with symmetric electrode configuration

Graduated optical filters are commonly used for spatial image control as they are capable of darkening the overexposed parts of the image specifically. However, they lack flexibility because each filter has a fixed transmission distribution. We herein present a fully controllable graduated filter based on the electrochromic device. Its graduated transmission distribution can be spatially controlled by the application of multiple electric potentials. In this way, the control of the gradient’s position and its width, transmission and angular orientation is possible. Simulation of both the spatial potential distribution and the resultant optical absorption distribution are conducted to optimize the electrode configuration and furthermore to derive a control dataset that facilitates the adjustment and thus the application of the graduated filter. Based on three objective and quantitative criteria, we identify the electrode configuration with the highest flexibility in all four controls, manufacture the device using a gravure printing process for the nanoparticle electrodes and show its successful application