In mathematics a positive map is a map between C*-algebras that sends positive elements to positive elements. A completely positive map is one that satisfies...

In mathematics, Choi's theorem on completely positive maps is a result that classifies completely positive maps between finite-dimensional (matrix) C*-algebras...

mechanical system. Rigorously, a quantum operation is a linear, completely positive map from the set of density operators into itself. In the context of...

The term positive map may refer to: Positive-definite functions in classical analysis Choi's theorem on completely positive maps between C*-algebras (pronounced...

operator theory that represents any completely positive map on a C*-algebra A as a composition of two completely positive maps each of which has a special form:...

the Internet. Terminologically, quantum channels are completely positive (CP) trace-preserving maps between spaces of operators. In other words, a quantum...

formalism (also known as a quantum dynamical map), which is a linear, trace-preserving, and completely positive map from the set of density matrices to itself...

any completely positive linear map from any self adjoint closed subspace containing 1 of any unital C*-algebra A to M can be extended to a completely positive...

linear operators. Sometimes the term refers more specially to a completely positive map which also preserves or does not increase the trace of its argument...

refers to the correspondence between quantum channels (described by completely positive maps) and quantum states (described by density matrices), this is introduced...

Y} are normed vector spaces, with the property that T {\displaystyle T} maps bounded subsets of X {\displaystyle X} to relatively compact subsets of Y...

isomorphism between completely positive maps (channels) from A to Cn×n, where A is a C*-algebra and Cn×n denotes the n×n complex entries, and positive linear functionals...

information theory. The Petz recovery map is a completely positive map, since (i) sandwiching by the positive semi-definite operator E ( σ ) − 1 / 2...

{E}}(\sigma ))\geq F(\rho ,\sigma ),} for any trace-preserving completely positive map E {\displaystyle {\mathcal {E}}} . We can define the trace distance...

Arveson's work on completely positive maps. One of his earlier results in this area is an extension theorem for completely positive maps with values in the...

physical resources independent of the input state to implement—a completely positive map. A corollary is that there is a physical process capable of broadcasting...

ensured by requiring that the time evolution is a trace-preserving, completely positive map.) The Born rule was formulated by Born in a 1926 paper. In this...

identity. The Stinespring factorization theorem characterizing completely positive maps is an important generalization of the GNS construction. Gelfand...

{\displaystyle {\mathcal {E}}(\rho )} , can be described by a completely positive map E ( ρ ) = ∑ i A i ρ A i † {\displaystyle {\mathcal {E}}(\rho )=\sum...

|^{2}}}=|i\rangle \langle i|.} We can define a linear, trace-preserving, completely positive map, by summing over all the possible post-measurement states of a...

based on an axiomatic approach. The basic starting point is a completely positive map. The assumption is that the initial system-environment state is...

measured again.: 91  We can define a linear, trace-preserving, completely positive map, by summing over all the possible post-measurement states of a...

Google maps, which is designed to offer a seven-day average data of the total COVID-19-positive cases per 100,000 people in the area selected on the map. It...

the ability to take adjoints of linear maps. Considering only the morphisms that are completely positive maps, one can also handle mixed states, allowing...

context of completely positive maps, especially when they represent quantum operations. If ϕ {\displaystyle \phi } is completely positive, it can always...

all positive map Φ, ( I ⊗ Φ ) ( ρ ) ≥ 0. {\displaystyle (I\otimes \Phi )(\rho )\geq 0.} Thus every positive, but not completely positive, map Φ gives rise...

positive but not completely positive maps can be naturally generalized from the bipartite case, as follows. Any positive but not completely positive (PnCP)...

{C} 1} . The appropriate morphisms between operator systems are completely positive maps. By a theorem of Choi and Effros, operator systems can be characterized...

theory) Browder–Minty theorem (operator theory) Choi's theorem on completely positive maps (operator theory) Commutation theorem (von Neumann algebra) Fuglede's...

\left\{{\mathcal {E}}_{x}\right\}} , for which the trace-non-increasing completely positive maps (CPMs) E x {\displaystyle {\mathcal {E}}_{x}} are local for all...