Leggett–Garg inequalities for a quantum top affected by classical noise

Leggett–Garg inequalities for a quantum top affected by classical noise 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Leggett–Garg inequalities for a quantum top affected by classical noise

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Publisher
Springer US
Copyright
Copyright © 2016 by The Author(s)
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1401-1
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 1, 2016

References

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