Appears in collection : 2017 - T3 - WS1 - Operator algebras and quantum information theory

QFA was a direct outgrowth of the Heisenberg and von Neumann notions of quantized random variables. Thus, one replaces n-tuples of reals by collections of (generally unbounded) real functions on a locally compact space by unbounded self-adjoint operators. In turn, completely bounded mappings play the role of classical operators. Using ingenious replacements for such notions as the central limit theorem, it is possible to find non-commutative (i. e. . “quantum”) analogues of much of functional analysis. These developments are particularly striking when considers the tensor products of operator spaces.