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===Degradation of a quantum reference frame ===
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|last1=Ahmadi|first1=Mehdi|last2=Jennings|first2=David|arxiv=1005.0798|doi=10.1103/PhysRevA.82.032320|last3=Rudolph|first3=Terry|year = 2010| bibcode=2010PhRvA..82c2320A | s2cid=119270210 }}</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-link=Terry Rudolph |author2=Rudolph, Terry|author3-link=Robert Spekkens |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 |s2cid=118880279 }}</ref>
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