In quantum mechanics, a quantum process is a somewhat ambiguous term which usually refers to the time evolution of an (open) quantum system. Under very general assumptions, a quantum process is described by the quantum operation 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.
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;[1][2] in principle, the density matrix of a quantum system can undergo completely arbitrary time evolution.
^Pechukas, Philip (1994). "Reduced Dynamics Need Not Be Completely Positive". Physical Review Letters. 73 (8): 1060–1062. Bibcode:1994PhRvL..73.1060P. doi:10.1103/PhysRevLett.73.1060. ISSN 0031-9007. PMID 10057614.
^Shaji, Anil; Sudarshan, E.C.G. (2005). "Who's afraid of not completely positive maps?". Physics Letters A. 341 (1–4). Elsevier BV: 48–54. Bibcode:2005PhLA..341...48S. doi:10.1016/j.physleta.2005.04.029. ISSN 0375-9601.
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