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One can observe that a ''z'' direction used in a laboratory in Berlin is generally totally different from a ''z'' direction used in a laboratory in Melbourne. Two laboratories trying to establish a single shared reference frame will face important issues involving alignment. The study of this sort of communication and coordination is a major topic in [[quantum information theory]].
Just as in this [[spin-1/2]] particle example, quantum reference frames are almost always treated implicitly in the definition of quantum states, and the process of including the reference frame in a quantum state is called quantisation/internalisation of reference frame while the process of excluding the reference frame from a quantum state is called dequantisation{{Citation needed|reason="Dequantisation" does not appear to be a common term in this field when applied to reference frames. Please find an example in the literature.|date=April 2014}}/externalisation of reference frame. Unlike the classical case, in which treating a reference internally or externally is purely an aesthetic choice, internalising and externalising a reference frame does make a difference in quantum theory.<ref>{{cite journal|last=Barlett|first=Stephen D. |author2=Rudolph, Terry |author3=Spekkens, Robert W.|title=Dialogue concerning two views on quantum coherences: factist and fictionist|journal=International Journal of Quantum Information|volume=4 |page=17|year=2006|bibcode=2005quant.ph..7214B |arxiv=quant-ph/0507214 |doi=10.1142/S0219749906001591 |s2cid=16503770 }}</ref>
One final remark may be made on the existence of a quantum reference frame. After all, a reference frame, by definition, has a well-defined position and momentum, while quantum theory, namely [[uncertainty principle]], states that one cannot describe any quantum system with well-defined position and momentum simultaneously, so it seems there is some contradiction between the two. It turns out, an effective frame, in this case a classical one, is used as a reference frame, just as in Newtonian mechanics a nearly inertial frame is used, and physical laws are assumed to be valid in this effective frame. In other words, whether motion in the chosen reference frame is inertial or not is irrelevant.
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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|
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>
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 | s2cid = 8337465}}</ref>
==References==
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