2019/01/20 by Joseph Avron, J. Avron, Oded Kenneth +1 · 1 voice · 2 citations
Physics and Astronomy · Mathematics · Computer Science · #Quantum Mechanics and Applications #Algebraic and Geometric Analysis #Quantum Information and Cryptography
paper · pdf · doi:10.1142/s0129055x20300010
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 [Formula: see text] qubits, the dimension is exponentially large in [Formula: see text]. 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. “All convex bodies behave a bit like Euclidean balls.” Keith Ball