The violation of the Leggett–Garg inequality is studied for a quantum top (with angular momentum $$J_z$$ J z of integer or half-integer size), being driven by classical Gaussian white noise. The form of a longitudinal $$(J_z)$$ ( J z ) or a transverse $$(J_x)$$ ( J x ) coupling of noise to the angular momentum affects both (i) to what extent the Leggett–Garg inequality is violated and (ii) how this violation is influenced by the size j of the spinning top and direction of a coupling (transverse or longitudinal). We introduce j-independent method, using two- dimensional invariant subspace of the system Hilbert space, which allows us to find out strict analytical solution for a noise-free system and with longitudinal coupling and to extract from the whole dynamics effects purely induced by a noise. It is demonstrated that in the semi-classical limit of a large angular momentum j and for the transverse coupling, the Leggett–Garg inequalities become more strongly violated as compared to the deep quantum regime of small j.
Quantum Information Processing – Springer Journals
Published: Aug 1, 2016
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