Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing. II. Applications to atomic magnetometry and Hardy's paradox

TL;DR

This paper extends quantum smoothing theory to include discrete jumps and variables, applying it to atomic magnetometry and Hardy's paradox, revealing phase-space negativity as key to quantum-classical discrepancies.

Contribution

It introduces an extended smoothing framework for discrete quantum variables and Poissonian measurements, with applications to magnetometry and foundational quantum paradoxes.

Findings

Negativity of the Wigner distribution explains quantum-classical disagreements.

Extended smoothing models discrete jumps and variables in quantum systems.

Application to atomic magnetometry improves understanding of measurement processes.

Abstract

The quantum smoothing theory [Tsang, Phys. Rev. Lett. 102, 250403 (2009); Phys. Rev. A, in press (e-print arXiv:0906.4133)] is extended to account for discrete jumps in the classical random process to be estimated, discrete variables in the quantum system, such as spin, angular momentum, and photon number, and Poissonian measurements, such as photon counting. The extended theory is used to model atomic magnetometers and study Hardy's paradox in phase space. In the phase-space picture of Hardy's proposed experiment, the negativity of the predictive Wigner distribution is identified as the culprit of the disagreement between classical reasoning and quantum mechanics.