Visualizing Entanglement in multi-Qubit Systems

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 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.

arXiv comment22 pages, 20 figures

References in corpus (25)

• Quantum entanglement
• Advances in Quantum Teleportation
• Topological Quantum Distillation
• Quantum Information and Relativity Theory
• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• Qudits and high-dimensional quantum computing
• Entanglement Measures under Symmetry
• Geometric Quantum Mechanics
• Entanglement in Quantum Information Theory
• Unfolding the color code
• The ZX-calculus is complete for stabilizer quantum mechanics
• Entangled Bloch Spheres: Bloch Matrix and Two Qubit State Space
• ZH: A Complete Graphical Calculus for Quantum Computations Involving Classical Non-linearity
• Visualizing operators of coupled spin systems
• Universal qudit gate synthesis for transmons
• Generalised phase kick-back: the structure of computational algorithms from physical principles
• Experimental exploration of five-qubit quantum error correcting code with superconducting qubits
• The interdisciplinary quantum information classroom: Themes from a survey of quantum information science instructors
• N-qubit states as points on the Bloch sphere
• Quantum Teleportation-Inspired Algorithm for Sampling Large Random Quantum Circuits
• Geometry of entanglement in the Bloch sphere
• Nested-sphere description of the N-level Chern number and the generalized Bloch hypersphere
• Time evolution of coupled spin systems in a generalized Wigner representation
• "Quantum supremacy" revisited: Low-complexity, deterministic solutions of the original Deutsch-Jozsa problem in classical physical systems
• Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems

Cited by in corpus (6)

• A Framework for Curriculum Transformation in Quantum Information Science and Technology Education
• Introducing Quantum Information and Computation to a Broader Audience with MOOCs at OpenHPI
• Exploring the mechanisms of qubit representations and introducing a new category system for visual representations: Results from expert ratings
• An Open-Source Data Storage and Visualization Platform for Collaborative Qubit Control
• Visualizing Quantum States: A Pilot Study on Problem Solving in Quantum Information Science Education
• Adiabatic Dynamics of Entanglement