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In mathematics, Choi's theorem on completely positive maps is a result that classifies completely positive maps between finite-dimensional (matrix) C*-algebras. An infinite-dimensional algebraic generalization of Choi's theorem is known as Belavkin 's "Radon–Nikodym" theorem for completely positive maps.
The Choi-Jamiołkowski isomorphism is a mathematical concept that connects quantum gates or operations to quantum states called Choi states. It allows us to represent a gate's properties and behavior as a Choi state. In the generalised gate teleportation scheme, we can teleport a quantum gate from one location to another using entangled states ...
Mathematically, a quantum operation is a linear map Φ between spaces of trace class operators on Hilbert spaces H and G such that. If S is a density operator, Tr (Φ (S)) ≤ 1. Φ is completely positive, that is for any natural number n, and any square matrix of size n whose entries are trace-class operators and which is non-negative, then is ...
Quantum channel. In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the general dynamics of a qubit. An example of classical information is a text document transmitted over the Internet.
Stinespring's theorem says that all completely positive maps are compositions of *-homomorphisms and these special maps. Every positive functional (in particular every state) is automatically completely positive. Given the algebras and of complex-valued continuous functions on compact Hausdorff spaces , every positive map is completely positive.
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose —that is, the element in the i -th row and j -th column is equal to the complex conjugate of the element in the j -th row and i -th column, for all indices i and j: or in matrix form:
Build The Earth was created by YouTuber PippenFTS in March 2020 as a collaborative effort to recreate Earth in the video game Minecraft. [1] During the COVID-19 lockdowns, the server aimed to provide players with the opportunity to virtually experience and construct the world. In a YouTube video, PippenFTS called for prospective participants to ...
Redfield equation. In quantum mechanics, the Redfield equation is a Markovian master equation that describes the time evolution of the reduced density matrix ρ of a strongly coupled quantum system that is weakly coupled to an environment. The equation is named in honor of Alfred G. Redfield, who first applied it, doing so for nuclear magnetic ...