Uncertainty — Quantum and Classical

John Peslak

A comparison of classical and quantum uncertainties is presented for the particle-in-a-box, the harmonic oscillator, and the one-electron atom. It is found that the quantum results reduce to the classical in the limit of either very large quantum numbers or h→0. A classical uncertainty principle is derived and compared with its quantum analogue. A possible relationship between zero-point motion and the uncertainty principle is noted.

Shunlong Luo

Pieter Kok

Yajing Fan, Nan Li, Shunlong Luo

It is important to distinguish between classical information and quantum information in quantum information theory. In this paper, we first extend the concept of metric-adjusted correlation measure and some related measures to non-Hermitian operators, and establish several relations between the metric-adjusted skew information with different operator monotone functions. By employing operator monotone functions, we next introduce three uncertainty matrices generated by channels: the total uncertainty matrix, the classical uncertainty matrix, and the quantum uncertainty matrix. We establish a decomposition of the total uncertainty matrix into classical and quantum parts and further investigate their basic properties. As applications, we employ uncertainty matrices to quantify the decoherence caused by the action of quantum channels on quantum states, and calculate the uncertainty matrices of some typical channels to reveal certain intrinsic features of the corresponding channels. Moreover, we establish several uncertainty relations that improve the traditional Heisenberg uncertainty relations involving variance.

William M. Honig, Kraft, David W, Panarella, Emilio

A.‐B. A. Mohamed, Ahmad N. Khedr, S. M. Younis

Abstract How the dynamics of classical and quantum correlations due to the Unruh effect are reflected in the properties of tripartite entropic uncertainty is investigated. It is found that, despite the quantum correlations disappearing at the limit of infinite acceleration, the uncertainty about the measurement outcome is at its minimum. This is due to the three‐qubit system still containing classic correlations at that stage of acceleration. Additionally, the decrease in the entropic uncertainty when the measured qubit interacts strongly with the scalar field can be attributed to the increase in classical correlations. Furthermore, it is found that the entropic uncertainty is fully anti‐correlated to classical correlations, and minimal uncertainty can be obtained even in the absence of quantum correlations. A tremendously tight constraint that effectively defined the properties of tripartite entropic uncertainty based on the difference between the total correlation and the Holevo quantities is achieved.