Editing Quantum Zeno effect (section)

{{Short description|Quantum measurement phenomenon}}
[[File:Quantum Zeno effect animation.gif|thumb|400px|With the increasing number of measurements the wave function tends to stay in its initial form. In the animation, a free time evolution of a wave function, depicted on the left, is in the central part interrupted by occasional position measurements that localize the wave function in one of nine sectors. On the right, a series of very frequent measurements leads to the quantum Zeno effect.]]
In [[quantum mechanics]], frequent measurements cause the '''quantum Zeno effect''', a reduction in transitions away from the systems initial state, slowing a systems [[time evolution]].<ref name=Facchi-2008/>{{rp|5}}

Sometimes this effect is interpreted as "a system cannot change while you are watching it".<ref>https://phys.org/news/2015-10-zeno-effect-verifiedatoms-wont.html. {{Webarchive|url=https://web.archive.org/web/20180925172404/https://phys.org/news/2015-10-zeno-effect-verifiedatoms-wont.html |date=2018-09-25 }}</ref> One can "freeze" the evolution of the system by measuring it frequently enough in its known initial state. The meaning of the term has since expanded, leading to a more technical definition, in which time evolution can be suppressed not only by measurement: the quantum Zeno effect is the suppression of unitary time evolution in [[quantum system]]s provided by a variety of sources: measurement, interactions with the environment, [[Stochastic process|stochastic fields]], among other factors.<ref name=Nakanishi>
{{cite journal
 |last1=Nakanishi |first1=T.
 |last2=Yamane |first2=K.
 |last3=Kitano |first3=M.
 |year=2001
 |title=Absorption-free optical control of spin systems: the quantum Zeno effect in optical pumping
 |journal=[[Physical Review A]]
 |volume=65 |issue=1 |page=013404
 |arxiv=quant-ph/0103034
 |bibcode=2001PhRvA..65a3404N
 |doi=10.1103/PhysRevA.65.013404
|s2cid=56052019
 }}</ref> As an outgrowth of study of the quantum Zeno effect, it has become clear that applying a series of sufficiently strong and fast pulses with appropriate symmetry can also ''decouple'' a system from its [[Quantum decoherence|decohering]] environment.<ref name=Facchi0>
{{cite journal
 |last1=Facchi |first1=P.
 |last2=Lidar |first2=D. A.
 |last3=Pascazio |first3=S.
 |year=2004
 |title=Unification of dynamical decoupling and the quantum Zeno effect
 |journal=[[Physical Review A]]
 |volume=69 |issue=3 |page=032314
 |arxiv=quant-ph/0303132
 |bibcode=2004PhRvA..69c2314F
 |doi=10.1103/PhysRevA.69.032314
|s2cid=38253718
 }}</ref>

The comparison with Zeno's paradox is due to a 1977 article by Baidyanath Misra & [[E. C. George Sudarshan]]. The name comes by analogy to [[Zeno's arrow paradox]], which states that because an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all. In the quantum Zeno effect an unstable state seems frozen – to not 'move' – due to a constant series of observations.

According to the reduction postulate, each measurement causes the [[wavefunction]] to [[wavefunction collapse|collapse]] to an [[eigenstate]] of the measurement basis. In the context of this effect, an ''observation'' can simply be the ''absorption'' of a particle, without the need of an observer in any conventional sense. However, there is controversy over the interpretation of the effect, sometimes referred to as the "[[measurement problem]]" in traversing the interface between microscopic and macroscopic objects.<ref name="Zajonc">{{cite book
 |last1=Greenstein |first1=G.
 |last2=Zajonc |first2=A.
 |year=2005
 |title=The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics
 |url=https://books.google.com/books?id=5t0tm0FB1CsC&q=%22quantum+Zeno%22&pg=PA231
 |page=237
 |publisher=[[Jones & Bartlett Publishers]]
 |isbn=978-0-7637-2470-2
}}</ref><ref name="Facchi">{{Cite journal
 |last1=Facchi |first1=P.
 |last2=Pascazio |first2=S.
 |year=2002
 |title=Quantum Zeno subspaces
 |journal=[[Physical Review Letters]]
 |volume=89 |issue=8 |page=080401
 |arxiv=quant-ph/0201115
 |bibcode=2002PhRvL..89h0401F
 |doi=10.1103/PhysRevLett.89.080401
|pmid=12190448
 |s2cid=29178016
 }}</ref>

Another crucial problem related to the effect is strictly connected to the [[Uncertainty principle#Time–energy uncertainty relation|time–energy indeterminacy relation]] (part of the [[indeterminacy principle]]). If one wants to make the measurement process more and more frequent, one has to correspondingly decrease the time duration of the measurement itself. But the request that the measurement last only a very short time implies that the energy spread of the state in which reduction occurs becomes increasingly large. However, the deviations from the [[exponential decay]] law for small times is crucially related to the inverse of the energy spread, so that the region in which the deviations are appreciable shrinks when one makes the measurement process duration shorter and shorter. An explicit evaluation of these two competing requests shows that it is inappropriate, without taking into account this basic fact, to deal with the actual occurrence and emergence of Zeno's effect.<ref name=Ghirardi>
{{cite journal
 |last1=Ghirardi |first1=G. C.
 |last2=Omero |first2=C.
 |last3=Rimini |first3=A.
 |last4=Weber |first4=T.
 |year=1979
 |title=Small Time Behaviour of Quantum Nondecay Probability and Zeno's Paradox in Quantum Mechanics
 |journal=[[Il Nuovo Cimento A]]
 |volume=52 |issue=4 |page=421
 |bibcode=1979NCimA..52..421G
 |doi=10.1007/BF02770851
|s2cid=124911216
 }}</ref>

Closely related (and sometimes not distinguished from the quantum Zeno effect) is the ''watchdog effect'', in which the time evolution of a system is affected by its continuous coupling to the environment.<ref>{{Cite journal |last=Kraus |first=K. |date=1981-08-01 |title=Measuring processes in quantum mechanics I. Continuous observation and the watchdog effect |journal=Foundations of Physics |language=en |volume=11 |issue=7–8 |pages=547–576 |doi=10.1007/bf00726936 |issn=0015-9018 |bibcode=1981FoPh...11..547K|s2cid=121902392 }}</ref><ref name=Belavkin-Staszewski>
{{cite journal
 | title = Nondemolition observation of a free quantum particle
 | last1 = Belavkin | first1 = V.
 | last2 = Staszewski | first2 = P.
 | journal = Phys. Rev. A
 | volume = 45
 | issue = 3
 | pages = 1347–1356
 | year = 1992
 | doi = 10.1103/PhysRevA.45.1347
 | pmid = 9907114 |bibcode = 1992PhRvA..45.1347B | arxiv = quant-ph/0512138| s2cid = 14637898 }}</ref><ref name=watchdog>
{{cite book
 |last1=Ghose |first1=P.
 |year=1999
 |title=Testing Quantum Mechanics on New Ground
 |url=https://books.google.com/books?id=GqRQYEPZRywC&q=%22watchdog+effect%22&pg=PA114
 |page=114
 |publisher=[[Cambridge University Press]]
 |isbn=978-0-521-02659-8
}}</ref><ref name=Auletta>
{{cite book
 |last1=Auletta |first1=G. |author1-link=Gennaro Auletta
 |year=2000
 |title=Foundations and Interpretation of Quantum Mechanics
 |url=https://books.google.com/books?id=lSAfY0LEKBMC&q=%22watchdog+effect%22&pg=RA1-PA341
 |page=341
 |publisher=[[World Scientific]]
 |isbn=978-981-02-4614-3
}}</ref>