An elementary introduction to the geometry of quantum states with pictures
arXiv:1901.06688 · doi:10.1142/S0129055X20300010
Abstract
This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The space of states can be visualized, to some extent, by its simple cross sections: Regular simplexes, balls and hyper-octahedra. When the dimension gets large there is a precise sense in which the space of states resembles, almost in every direction, a ball. The ball turns out to be a ball of rather low purity states. We also address some of the corresponding, but harder, geometric properties of separable and entangled states and entanglement witnesses.
arXiv comment35 pages, 16 figures, ref and typo corrected
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- Quantum State Reconstruction in a Noisy Environment via Deep Learning
- Maximum Geometric Quantum Entropy
- Geometry of entanglement and separability in Hilbert subspaces of dimension up to three
- Robust entanglement measure for mixed quantum states
- Matrix convex sets over the Euclidean ball and polar duals of real free spectrahedra