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Visualizing two qubits
Abstract
I propose a simple visualization for pure two-qubit states, constructed from three components: two Bloch balls for the marginal qubits (the mixed states obtained by ignoring the other qubit, respectively) and an entanglement component consisting of a rotoreflection and a contraction. I prove that this picture accurately captures the local and global structure of the relevant state space without gaps or degeneracies: the underlying parametrization is a global diffeomorphism onto the state space. Finally, I use this picture to visualize conditional states, the entanglement degree(s) of freedom, and single qubit rotations.
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BibTeX
@misc{grosseholz2026visualizing,
title = {{Visualizing two qubits}},
author = {Simon Grosse-Holz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08897},
eprint = {2610.08897},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08897},
}
RIS
TY - UNPB
TI - Visualizing two qubits
AU - Simon Grosse-Holz
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08897
UR - https://arxiv.org/abs/2610.08897
AB - I propose a simple visualization for pure two-qubit states, constructed from three components: two Bloch balls for the marginal qubits (the mixed states obtained by ignoring the other qubit, respectively) and an entanglement component consisting of a rotoreflection and a contraction. I prove that this picture accurately captures the local and global structure of the relevant state space without gaps or degeneracies: the underlying parametrization is a global diffeomorphism onto the state space. Finally, I use this picture to visualize conditional states, the entanglement degree(s) of freedom, and single qubit rotations.
ER -