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Dynamics of ‘quantumness’ measures in the decohering harmonic oscillator

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Abstract

We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of all classical states. The fourth measure is an absolute one, the negative volume of the Wigner function of the state. All four measures are found to agree, in general, with each other. When applied to the eigenstates |n〉, all four measures behave non-trivially as a function of time during dynamical decoherence. First, we find that the first set of classical states to which the set of eigenstate evolves is (by all measures used) closest to the initial set. That is, all the states decohere to classicality along the ‘shortest path’. Finding this closest classical set of states helps improve the behaviour of all the relative distance measures. Second, at each point in time before becoming classical, all measures have a state n ∗ with maximal quantum-classical distance; the value n ∗ decreases as a function of time. Finally, we explore the dynamics of these non-classicality measures for more general states.

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Acknowledgements

It is a pleasure to thank Prof. Howard Wiseman for very useful and encouraging comments, as well as the funding from the Howard Hughes Medical Institute through Carleton College.

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Authors and Affiliations

  1. Department of Physics and Astronomy, Carleton College, One North College Street, Northfield, MN, 55057, USA

    PETER A ROSE, ANDREW C McCLUNG, TYLER E KEATING, ADAM T C STEEGE & ARJENDU K PATTANAYAK

  2. Department of Mathematics, Carleton College, One North College Street, Northfield, MN, 55057, USA

    ERIC S EGGE

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  1. PETER A ROSE
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  2. ANDREW C McCLUNG
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  3. TYLER E KEATING
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  4. ADAM T C STEEGE
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Correspondence to ARJENDU K PATTANAYAK.

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ROSE, P.A., McCLUNG, A.C., KEATING, T.E. et al. Dynamics of ‘quantumness’ measures in the decohering harmonic oscillator. Pramana - J Phys 87, 32 (2016). https://doi.org/10.1007/s12043-016-1229-3

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  • DOI: https://doi.org/10.1007/s12043-016-1229-3

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