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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.
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 ...
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.
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 ...
Quantum depolarizing channel. A quantum depolarizing channel is a model for quantum noise in quantum systems. The -dimensional depolarizing channel can be viewed as a completely positive trace-preserving map , depending on one parameter , which maps a state onto a linear combination of itself and the maximally mixed state, The condition of ...
The partial trace is performed over a subsystem of 2 by 2 dimension (single qubit density matrix). The right hand side shows the resulting 2 by 2 reduced density matrix . In linear algebra and functional analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar valued function on operators, the partial trace is ...
Lindbladian. In quantum mechanics, the Gorini–Kossakowski–Sudarshan–Lindblad equation (GKSL equation, named after Vittorio Gorini, Andrzej Kossakowski, George Sudarshan and Göran Lindblad), master equation in Lindblad form, quantum Liouvillian, or Lindbladian is one of the general forms of Markovian master equations describing open ...
Levi-Civita connection. In Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves the (pseudo-) Riemannian metric and is torsion -free.