Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Frames of Reference and the Noncommutative Values of Observables   Based on a recent relational formulation of quantum reference frame
transformations, especially with a case of quantum spatial translations in
particular, we analyzed how the `value' of an observable for a fixed state
change. That is the exact analog of the classical description, for example, of
the value of the $x$-coordinate for a particle decrease by 2 units when we
perform a translation of the reference frame putting the new origin at $x=2$.
The essence of the quantum reference frame transformations is to have the
quantum fluctuations, and even entanglement, of the physical object which
serves as the (new) reference frame, taken into account. We illustrate how the
recently introduced notion of the noncommutative values of quantum observables
gives such a definite description successfully. Formulations, and an analysis
of a case example in qubit systems, of analog transformations for observables
with a discrete or finite spectrum is also presented. Issues about the evolving
picture of the symmetry system of all quantum reference frame transformations
discussed.

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The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: comp-gas