Ad
related to: hermitian trace preserving map
Search results
Results From The WOW.Com Content Network
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 ...
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 ...
Density matrices are specified to have trace 1, so has to preserve the trace. The adjectives completely positive and trace preserving used to describe a map are sometimes abbreviated CPTP . In the literature, sometimes the fourth property is weakened so that Φ {\displaystyle \Phi } is only required to be not trace-increasing.
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.
In quantum information theory and operator theory, the Choi–Jamiołkowski isomorphism refers to the correspondence between quantum channels (described by completely positive maps) and quantum states (described by density matrices), this is introduced by Man-Duen Choi [1] and Andrzej Jamiołkowski. [2] It is also called channel-state duality ...
The Weyl representation or spinor map is a pair of surjective homomorphisms from SL(2, C) to SO + (1, 3). They form a matched pair under parity transformations, corresponding to left and right chiral spinors. One may define an action of SL(2, C) on Minkowski spacetime by writing a point of spacetime as a two-by-two Hermitian matrix in the form
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.
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 complete positivity requires to ...