Physics:Quantum speed limit - Revision history

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	== Bremermann's limit ==		== Bremermann's limit ==
	~~{{main\|~~Bremermann's limit}}		''Related topic:'' Bremermann's limit

	The quantum speed limit bounds establish an upper bound at which computation can be performed. Computational machinery is constructed out of physical matter that follows quantum mechanics, and each operation, if it is to be unambiguous, must be a transition of the system from one state to an orthogonal state. Suppose the computing machinery is a physical system evolving under Hamiltonian that does not change with time. Then, according to the Margolus–Levitin theorem, the number of operations per unit time per unit energy is bounded above by		The quantum speed limit bounds establish an upper bound at which computation can be performed. Computational machinery is constructed out of physical matter that follows quantum mechanics, and each operation, if it is to be unambiguous, must be a transition of the system from one state to an orthogonal state. Suppose the computing machinery is a physical system evolving under Hamiltonian that does not change with time. Then, according to the Margolus–Levitin theorem, the number of operations per unit time per unit energy is bounded above by

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	The [[Astronomy:Bekenstein bound\|Bekenstein bound]] limits the amount of information that can be stored within a volume of space. The maximal rate of change of information within that volume of space is given by the quantum speed limit. This product of limits is sometimes called the '''Bremermann–Bekenstein limit'''; it is saturated by [[Physics:Hawking radiation\|Hawking radiation]].<ref name="DEF"/> That is, Hawking radiation is emitted at the maximal allowed rate set by these bounds.		The [[Astronomy:Bekenstein bound\|Bekenstein bound]] limits the amount of information that can be stored within a volume of space. The maximal rate of change of information within that volume of space is given by the quantum speed limit. This product of limits is sometimes called the '''Bremermann–Bekenstein limit'''; it is saturated by [[Physics:Hawking radiation\|Hawking radiation]].<ref name="DEF"/> That is, Hawking radiation is emitted at the maximal allowed rate set by these bounds.

			== See also ==
			{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	== References ==		== References ==
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	[[Category:Mathematical physics]]		[[Category:Mathematical physics]]

	{{Sourceattribution\|Quantum speed limit}}		{{Author\|Harold Foppele}}

			{{Sourceattribution\|Physics:Quantum speed limit\|1}}

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	[[File:Speed Limit Quatum.png]]		[[File:Speed Limit Quatum.png\|thumb\|280px\|A quantum speed limit sets a minimum time for a quantum state to evolve into a distinguishable state, linking the pace of quantum change to energy uncertainty and available energy.]]
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 {{Quantum book backlink|Quantum dynamics and evolution}}
 In [[Physics:Quantum mechanics|quantum mechanics]], a '''quantum speed limit''' ('''QSL''') is a limitation on the minimum time for a quantum system to evolve between two distinguishable (orthogonal) states.<ref name="DEF">{{cite journal |last1=Deffner |first1=S. |last2=Campbell |first2=S. |title=Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control |journal=J. Phys. A: Math. Theor. |date=10 October 2017 |volume=50 |issue=45 |page=453001 |doi=10.1088/1751-8121/aa86c6|arxiv=1705.08023 |bibcode=2017JPhA...50S3001D |s2cid=3477317 }}</ref> QSL theorems are closely related to time-energy uncertainty relations. In 1945, [[Biography:Leonid Mandelstam|Leonid Mandelstam]] and [[Biography:Igor Tamm|Igor Tamm]] derived a time-energy uncertainty relation that bounds the speed of evolution in terms of the energy dispersion.<ref name="MTT">{{cite journal |last1=Mandelshtam |first1=L. I. |last2=Tamm |first2=I. E. |title=The uncertainty relation between energy and time in nonrelativistic quantum mechanics |journal=J. Phys. (USSR) |date=1945 |volume=9 |pages=249–254}} Reprinted as {{cite book |chapter=The Uncertainty Relation Between Energy and Time in Non-relativistic Quantum Mechanics |date=1991 |title=Selected Papers |pages=115–123 |editor-last=Bolotovskii |editor-first=Boris M. |url=http://link.springer.com/10.1007/978-3-642-74626-0_8 |access-date=2024-04-06 |place=Berlin, Heidelberg |publisher=Springer |language=en |doi=10.1007/978-3-642-74626-0_8 |isbn=978-3-642-74628-4 |last1=Mandelstam |first1=L. |last2=Tamm |first2=Ig. |editor2-last=Frenkel |editor2-first=Victor Ya. |editor3-last=Peierls |editor3-first=Rudolf |editor-link3=Rudolf Peierls}}</ref> Over half a century later, [[Biography:Norman Margolus|Norman Margolus]] and [[Biography:Lev Levitin|Lev Levitin]] showed that the speed of evolution cannot exceed the mean energy,<ref name="Margolus1998">{{cite journal |last1=Margolus |first1=Norman |last2=Levitin |first2=Lev B. |title=The maximum speed of dynamical evolution |journal=Physica D: Nonlinear Phenomena |date=September 1998 |volume=120 |issue=1–2 |pages=188–195 |doi=10.1016/S0167-2789(98)00054-2 |arxiv=quant-ph/9710043 |bibcode=1998PhyD..120..188M |s2cid=468290 }}</ref> a result known as the Margolus–Levitin theorem. Realistic physical systems in contact with an environment are known as [[Physics:Open quantum system|open quantum system]]s and their evolution is also subject to QSL.<ref>{{cite journal |last1=Taddei |first1=M. M. |last2=Escher |first2=B. M. |last3=Davidovich |first3=L. |last4=de Matos Filho |first4=R. L. |title=Quantum Speed Limit for Physical Processes |journal=[[Physics:Physical Review Letters|Physical Review Letters]] |date=30 January 2013 |volume=110 |issue=5 |article-number=050402 |doi=10.1103/PhysRevLett.110.050402 |pmid=23414007 |arxiv=1209.0362 |bibcode=2013PhRvL.110e0402T |s2cid=38373815 }}</ref><ref>{{cite journal |last1=del Campo |first1=A. |last2=Egusquiza |first2=I. L. |last3=Plenio |first3=M. B. |last4=Huelga |first4=S. F. |date=30 January 2013 |title=Quantum Speed Limits in Open System Dynamics |journal=[[Physics:Physical Review Letters|Physical Review Letters]] |volume=110 |issue=5 |article-number=050403 |arxiv=1209.1737 |bibcode=2013PhRvL.110e0403D |doi=10.1103/PhysRevLett.110.050403 |pmid=23414008 |s2cid=8362503}}</ref> Quite remarkably it was shown that environmental effects, such as non-Markovian dynamics can speed up quantum processes,<ref>{{cite journal |last1=Deffner |first1=S. |last2=Lutz |first2=E. |title=Quantum speed limit for non-Markovian dynamics |journal=[[Physics:Physical Review Letters|Physical Review Letters]] |date=3 July 2013 |volume=111 |issue=1 |article-number=010402 |doi=10.1103/PhysRevLett.111.010402|pmid=23862985 |arxiv=1302.5069 |bibcode=2013PhRvL.111a0402D |s2cid=36711861 }}</ref> which was verified in a cavity QED experiment.<ref>{{cite journal |last1=Cimmarusti |first1=A. D. |last2=Yan |first2=Z. |last3=Patterson |first3=B. D. |last4=Corcos |first4=L. P. |last5=Orozco |first5= L. A. |last6=Deffner |first6=S. |title=Environment-Assisted Speed-up of the Field Evolution in Cavity Quantum Electrodynamics |journal=[[Physics:Physical Review Letters|Physical Review Letters]] |date=11 June 2015 |volume=114 |issue=23 |article-number=233602 |doi=10.1103/PhysRevLett.114.233602|pmid=26196802 |arxiv=1503.02591 |bibcode=2015PhRvL.114w3602C |s2cid=14904633 }}</ref>
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 In [[Quantum sensor|quantum sensing]], QSLs impose fundamental constraints on the maximum achievable time resolution of quantum sensors. These limits stem from the requirement that quantum states must evolve to orthogonal states to extract precise information. For example, in applications like [[Physics:Ramsey interferometry|Ramsey interferometry]], the QSL determines the minimum time required for phase accumulation during control sequences, directly impacting the sensor's [[Engineering:Temporal resolution|temporal resolution]] and sensitivity.<ref>{{cite journal |last1=Herb |first1=Konstantin | last2=Degen | first2=Christian L. |title=Quantum speed limit in quantum sensing |journal=[[Physics:Physical Review Letters|Physical Review Letters]] | date=19 November 2024 | volume=133 |issue=21 |article-number=210802|doi=10.1103/PhysRevLett.133.210802 |arxiv=2406.18348 }}</ref>
 == Preliminary definitions ==