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Sum rule of quantum uncertainties: coupled harmonic oscillator system with time-dependent parameters

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Abstract

Uncertainties \((\Delta x)^2\) and \((\Delta p)^2\) are analytically derived in an N-coupled harmonic oscillator system when spring and coupling constants are arbitrarily time-dependent and each oscillator is in an arbitrary excited state. When \(N = 2\), those uncertainties are shown as just arithmetic average of uncertainties of two single harmonic oscillators. We call this property as “sum rule of quantum uncertainty”. However, this arithmetic average property is not generally maintained when \(N \ge 3\), but it is recovered in N-coupled oscillator systems if and only if \((N-1)\) quantum numbers are equal. The generalization of our results to a more general quantum system is briefly discussed.

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Notes

  1. The Rényi-\(\alpha \) entropies of few non-Gaussian states have been derived in [29].

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Authors and Affiliations

  1. Department of Electronic Engineering, Kyungnam University, Changwon, 631-701, Korea

    DaeKil Park & Eylee Jung

  2. Department of Physics, Kyungnam University, Changwon, 631-701, Korea

    DaeKil Park

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Park, D., Jung, E. Sum rule of quantum uncertainties: coupled harmonic oscillator system with time-dependent parameters. Quantum Inf Process 19, 259 (2020). https://doi.org/10.1007/s11128-020-02757-8

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