Physics:Quantum process: Difference between revisions
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{{Short description|Time evolution of quantum systems}} | {{Short description|Time evolution of quantum systems}} | ||
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In [[Physics:Quantum mechanics|quantum mechanics]], a '''quantum process''' is a somewhat ambiguous term which usually refers to the time evolution of an ([[Physics:Open quantum system|open]]) quantum system. Under very general assumptions, a quantum process is described by the [[Physics:Quantum operation|quantum operation]] formalism (also known as a ''quantum dynamical map''), which is a [[Linear map|linear]], trace-preserving, and completely positive map from the set of [[Density matrix|density matrices]] to itself. | In [[Physics:Quantum mechanics|quantum mechanics]], a '''quantum process''' is a somewhat ambiguous term which usually refers to the time evolution of an ([[Physics:Open quantum system|open]]) quantum system. Under very general assumptions, a quantum process is described by the [[Physics:Quantum operation|quantum operation]] formalism (also known as a ''quantum dynamical map''), which is a [[Linear map|linear]], trace-preserving, and completely positive map from the set of [[Density matrix|density matrices]] to itself. | ||
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However, not all quantum processes can be captured within the quantum operation formalism;<ref>{{cite journal|last1=Pechukas|first1=Philip|title=Reduced Dynamics Need Not Be Completely Positive|journal=Physical Review Letters|volume=73|issue=8|year=1994|pages=1060–1062|issn=0031-9007|doi=10.1103/PhysRevLett.73.1060|pmid=10057614 |bibcode=1994PhRvL..73.1060P }}</ref><ref>{{cite journal | last1=Shaji | first1=Anil | last2=Sudarshan | first2=E.C.G. | title=Who's afraid of not completely positive maps? | journal=Physics Letters A | publisher=Elsevier BV | volume=341 | issue=1–4 | year=2005 | issn=0375-9601 | doi=10.1016/j.physleta.2005.04.029 | pages=48–54| bibcode=2005PhLA..341...48S }}</ref> in principle, the density matrix of a quantum system can undergo completely arbitrary time evolution. | However, not all quantum processes can be captured within the quantum operation formalism;<ref>{{cite journal|last1=Pechukas|first1=Philip|title=Reduced Dynamics Need Not Be Completely Positive|journal=Physical Review Letters|volume=73|issue=8|year=1994|pages=1060–1062|issn=0031-9007|doi=10.1103/PhysRevLett.73.1060|pmid=10057614 |bibcode=1994PhRvL..73.1060P }}</ref><ref>{{cite journal | last1=Shaji | first1=Anil | last2=Sudarshan | first2=E.C.G. | title=Who's afraid of not completely positive maps? | journal=Physics Letters A | publisher=Elsevier BV | volume=341 | issue=1–4 | year=2005 | issn=0375-9601 | doi=10.1016/j.physleta.2005.04.029 | pages=48–54| bibcode=2005PhLA..341...48S }}</ref> in principle, the density matrix of a quantum system can undergo completely arbitrary time evolution. | ||
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== References == | == References == | ||
Revision as of 21:53, 17 May 2026
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.
References
- ↑ Pechukas, Philip (1994). "Reduced Dynamics Need Not Be Completely Positive". Physical Review Letters 73 (8): 1060–1062. doi:10.1103/PhysRevLett.73.1060. ISSN 0031-9007. PMID 10057614. Bibcode: 1994PhRvL..73.1060P.
- ↑ Shaji, Anil; Sudarshan, E.C.G. (2005). "Who's afraid of not completely positive maps?". Physics Letters A (Elsevier BV) 341 (1–4): 48–54. doi:10.1016/j.physleta.2005.04.029. ISSN 0375-9601. Bibcode: 2005PhLA..341...48S.
- Nielsen, Michael A.; Chuang, Isaac L. (2010). Quantum Computation and Quantum Information (2nd ed.). Cambridge: Cambridge University Press. ISBN 978-1-107-00217-3. OCLC 844974180.
Source attribution: Quantum process
