Classicality versus quantumness in Born's probability

Shunlong Luo
Phys. Rev. A 96, 052126 – Published 20 November 2017

Abstract

Born's rule, which postulates the probability of a measurement outcome in a quantum state, is pivotal to interpretations and applications of quantum mechanics. By exploiting the departure of the product of two Hermitian operators in Born's rule from Hermiticity, we prescribe an intrinsic and natural scheme to decompose Born's probability into a classical part and a quantum part, which have significant implications in quantum information theory. The classical part constitutes the information compatible with the associated measurement operator, while the quantum part represents the quantum coherence of the state with respect to the measurement operator. Fundamental properties of the decomposition are revealed. As applications, we establish several trade-off relations for the classicality and quantumness in Born's probability, which may be interpreted as alternative realizations of Heisenberg's uncertainty principle. The results shed physical lights on related issues concerning quantification of complementarity, coherence, and uncertainty, as well as the classical-quantum interplay.

  • Received 21 May 2017

DOI:https://doi.org/10.1103/PhysRevA.96.052126

©2017 American Physical Society

Physics Subject Headings (PhySH)

General Physics

Authors & Affiliations

Shunlong Luo*

  • Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences, University of the Chinese Academy of Sciences, Beijing 100049, China

  • *luosl@amt.ac.cn

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Issue

Vol. 96, Iss. 5 — November 2017

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