Journal
REVIEWS IN MATHEMATICAL PHYSICS
Volume 32, Issue 2, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129055X20300010
Keywords
Geometry; quantum states; convexity; qubits; entanglement; separability; concentration of measure
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Funding
- ISF
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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.a 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.
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