Quantum reference frame: Difference between revisions

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As it turns out, the lack of a reference frame is mathematically equivalent to superselection rules. This is a powerful statement because superselection rules have long been thought to have axiomatic nature, and now its fundamental standing and even its necessity are questioned. Nevertheless, it has been shown that it is, in principle, always possible (though not always easy) to lift all superselection rules on a quantum system.

===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 so-called measurement [[Back action (quantum)|back reactionaction]]. As this process is repeated over time during a measurement, it negatively affectsdecreases the accuracy of the measurement outcomes, and the gradualsuch reduction of the usability of a reference frame is referred to as the degradation of a quantum reference frame<ref name=":0" />. 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 exceedexceeded.

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 exceedexceeded 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 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>

:::<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 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>{{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==