Visualizing Entanglement in multi-Qubit Systems
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arXiv
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| Main Authors: | , , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912094249549824 |
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| author | Bley, Jonas Rexigel, Eva Arias, Alda Longen, Nikolas Krupp, Lars Kiefer-Emmanouilidis, Maximilian Lukowicz, Paul Donhauser, Anna Küchemann, Stefan Kuhn, Jochen Widera, Artur |
| author_facet | Bley, Jonas Rexigel, Eva Arias, Alda Longen, Nikolas Krupp, Lars Kiefer-Emmanouilidis, Maximilian Lukowicz, Paul Donhauser, Anna Küchemann, Stefan Kuhn, Jochen Widera, Artur |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07596 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Visualizing Entanglement in multi-Qubit Systems Bley, Jonas Rexigel, Eva Arias, Alda Longen, Nikolas Krupp, Lars Kiefer-Emmanouilidis, Maximilian Lukowicz, Paul Donhauser, Anna Küchemann, Stefan Kuhn, Jochen Widera, Artur Quantum Physics 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. |
| title | Visualizing Entanglement in multi-Qubit Systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2305.07596 |