In
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, a quantum process is a somewhat ambiguous term which usually refers to the time evolution of an (
open
Open or OPEN may refer to:
Music
* Open (band), Australian pop/rock band
* The Open (band), English indie rock band
* ''Open'' (Blues Image album), 1969
* ''Open'' (Gotthard album), 1999
* ''Open'' (Cowboy Junkies album), 2001
* ''Open'' (YF ...
) quantum system. Under very general assumptions, a quantum process is described by the
quantum operation
In quantum mechanics, a quantum operation (also known as quantum dynamical map or quantum process) is a mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. This was first discusse ...
formalism (also known as a ''quantum dynamical map''), which is a
linear
Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...
, trace-preserving, and
completely positive
In mathematics a positive map is a map between C*-algebras that sends positive elements to positive elements. A completely positive map is one which satisfies a stronger, more robust condition.
Definition
Let A and B be C*-algebras. A linea ...
map from the set of
density matrices
In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any Measurement in quantum mechanics, measurement ...
to itself.
For instance, in
quantum process tomography, the unknown quantum process is assumed to be a quantum operation.
However, not all quantum processes can be captured within the quantum operation formalism;
in principle, the density matrix of a quantum system can undergo completely arbitrary time evolution.
References
*
Quantum mechanics
{{Quantum-stub