Visualizing entanglement in multiqubit systems
Jonas Bley, Eva Rexigel, Alda Arias, Nikolas Longen, Lars Krupp, Maximilian Kiefer-Emmanouilidis, Paul Lukowicz, Anna Donhauser, Stefan Küchemann, Jochen Kühn, Artur Widera
Abstract
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 lies especially on ensembles of few qubits. There exist many powerful representations for single-qubit and multiqubit 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>n</a:mi></a:math>-particle system in an <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>n</b:mi></b:math>-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. Published by the American Physical Society 2024