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During a measurement, whenever the relations between the system and the reference frame used is inquired, there is inevitably a disturbance to both of them, which is known as measurement [[Back action (quantum)|back action]]. As this process is repeated, it decreases the accuracy of the measurement outcomes, and such reduction of the usability of a reference frame is referred to as the degradation of a quantum reference frame.<ref name=":0" /><ref>{{Cite journal|title=Dynamics of a quantum reference frame undergoing selective measurements and coherent interactions|journal = Physical Review A|volume = 82|issue = 3|pages = 032320|last=Ahmadi|first=Mehdi|last2=Jennings|first2=David|arxiv=1005.0798|doi=10.1103/PhysRevA.82.032320|last3=Rudolph|first3=Terry|year = 2010}}</ref> A way to gauge the degradation of a reference frame is to quantify the longevity, namely, the number of measurements that can be made against the reference frame until certain error tolerance is exceeded.
For example, for a spin-<math>j</math> system, the maximum number of measurements that can be made before the error tolerance, <math>\epsilon</math>, is exceeded is given by <math>n_{max} \simeq \epsilon j^2</math>. So the longevity and the size of the reference frame are of quadratic relation in this particular case.<ref>{{cite journal|last=Bartlett|first=Stephen D. |author2=Rudolph, Terry |author3=Spekkens, Robert W.|title=Reference frames, superselection rules, and quantum information|journal=Reviews of Modern Physics|volume=79|issue=2|date=April–June 2007|pages=555–606|doi=10.1103/RevModPhys.79.555|bibcode=2007RvMP...79..555B|arxiv = quant-ph/0610030 }}</ref>
In this spin-<math>j</math> system, the degradation is due to the loss of purity of the reference frame state. On the other hand, degradation can also be caused by misalignment of background reference. It has been shown, in such case, the longevity has a linear relation with the size of the reference frame.<ref name=":0">{{cite journal| doi = 10.1088/1367-2630/9/5/156| last = Poulin| first = D. |author2=J. Yard | title = Dynamics of a quantum reference frame|year=2007|journal=New J. Phys.|volume = 9| issue = 5|pages=156|arxiv = quant-ph/0612126 |bibcode = 2007NJPh....9..156P }}</ref>
==References==
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