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In quantum physics and specifically in quantum computation/quantum information, Bloch region is the name of the convex space of density matrices on a given Hilbert space.
Equivalently this is the space of mixed quantum states for a quantum mechanical system with the lines in given Hilbert space as its pure states.
The superoperators that preserve Bloch regions (also for products, “complete positivity”) are called quantum operations.
For $(n+1) \in \mathbb{N}$ a natural number, the Bloch region in the $(n+1)$-dimensional Hilbert space $\mathbb{C}^{n+1}$ is a quantum physics-analog of the space of probability measures on the finite set of $(n+1)$ elements. This in turn is equivalently the standard $n$-simplex $\Delta^n$.
A quick introduction is in
Created on January 23, 2014 at 06:07:08. See the history of this page for a list of all contributions to it.