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A reference frame can be treated in the formalism of quantum theory, and, in this case, such is referred as a quantum reference frame. Despite different name and treatment, a quantum reference frame still shares much of the notions with a reference frame in [[classical mechanics]]. It is associated to some physical system, and it is [[Relational quantum mechanics|relational]].
For example, if a [[spin-1/2]] particle is said to be in the state <math>\left|\uparrow z \right\rangle</math>, a reference frame is implicitly implied, and it can be understood to be some reference frame with respect to an apparatus in a lab. It is obvious that the description of the particle does not place it in an absolute space, and doing so would make no sense at all because, as mentioned above, absolute space is empirically unobservable. On the other hand, if a magnetic field along y-axis is said to be given, the behaviour of the particle in such field can then be described. In this sense, ''y'' and ''z'' are just relative directions. They do not and need not have absolute meaning.
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]].
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