TY - JOUR

T1 - Quantum frames of reference and the noncommutative values of observables

AU - Kong, Otto C.W.

N1 - Publisher Copyright:
© 2021 The Author

PY - 2021/12

Y1 - 2021/12

N2 - 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.

AB - 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.

KW - Noncommutative values of observables

KW - Quantum frames of reference

UR - http://www.scopus.com/inward/record.url?scp=85120642383&partnerID=8YFLogxK

U2 - 10.1016/j.rinp.2021.105033

DO - 10.1016/j.rinp.2021.105033

M3 - 期刊論文

AN - SCOPUS:85120642383

VL - 31

JO - Results in Physics

JF - Results in Physics

SN - 2211-3797

M1 - 105033

ER -