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Quantum Information Processing

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

  • 01-08-2020
Published in:
Authors
DaeKil Park
Eylee Jung
Published in
Quantum Information Processing | Issue 8/2020

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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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Title
Sum rule of quantum uncertainties: coupled harmonic oscillator system with time-dependent parameters
Authors
DaeKil Park
Eylee Jung
Publication date
01-08-2020
Publisher
Springer US
Published in
Quantum Information Processing / Issue 8/2020
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-020-02757-8
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