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In quantum mechanics, each physical system is associated with a Hilbert space, each element of which represents a possible state of the physical system.The approach codified by John von Neumann represents a measurement upon a physical system by a self-adjoint operator on that Hilbert space termed an "observable".
The von Neumann–Wigner interpretation, also described as "consciousness causes collapse", is an interpretation of quantum mechanics in which consciousness is postulated to be necessary for the completion of the process of quantum measurement.
In mathematics, lifting theory was first introduced by John von Neumann in a pioneering paper from 1931, in which he answered a question raised by Alfréd Haar. [1] The theory was further developed by Dorothy Maharam (1958) [ 2 ] and by Alexandra Ionescu Tulcea and Cassius Ionescu Tulcea (1961). [ 3 ]
As Garrett Birkhoff wrote, "John von Neumann's brilliant mind blazed over lattice theory like a meteor". [168] Von Neumann combined traditional projective geometry with modern algebra (linear algebra, ring theory, lattice theory). Many previously geometric results could then be interpreted in the case of general modules over rings. His work ...
The formalism of density operators and matrices was introduced in 1927 by John von Neumann [29] and independently, but less systematically, by Lev Landau [30] and later in 1946 by Felix Bloch. [31] Von Neumann introduced the density matrix in order to develop both quantum statistical mechanics and a theory of quantum measurements.
In physics, the von Neumann entropy, named after John von Neumann, is a measure of the statistical uncertainty within a description of a quantum system.It extends the concept of Gibbs entropy from classical statistical mechanics to quantum statistical mechanics, and it is the quantum counterpart of the Shannon entropy from classical information theory.
The von Neumann description of quantum measurement of an observable A, when the system is prepared in a pure state ψ is the following (note, however, that von Neumann's description dates back to the 1930s and is based on experiments as performed during that time – more specifically the Compton–Simon experiment; it is not applicable to most ...
In quantum information theory, quantum mutual information, or von Neumann mutual information, after John von Neumann, is a measure of correlation between subsystems of quantum state. It is the quantum mechanical analog of Shannon mutual information .