Quantum to Classical Transitions via Weak Measurements and Post-Selection

TL;DR

This paper explores how classical phenomena emerge from quantum mechanics through the process of repeated weak measurements and post-selection, providing a quantitative boundary between quantum and classical regimes.

Contribution

It introduces a framework linking weak measurements and post-selection to the emergence of classical variables from quantum systems, offering a new perspective on quantum-classical transition.

Findings

Classical variables result from many quantum weak measurements.

A sequence of weak measurements can be viewed as a single projective measurement.

The work defines a quantitative boundary between quantum and classical regimes.

Abstract

This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based on a very weak von Neumann coupling, is a unique kind of quantum measurement with numerous theoretical and practical applications. In contrast to other measurement techniques, it allows to gather a small amount of information regarding the quantum system, with only a negligible probability of collapsing it. A single weak measurement yields an almost random outcome, but when performed repeatedly over a large ensemble, the averaged outcome becomes increasingly robust and accurate. Importantly, a long sequence of weak measurements can be thought of as a single projective measurement. I claim in this work that classical variables appearing in the macro-world, such as centre of mass, moment of inertia, pressure and average forces, result from a multitude of quantum weak measurements performed in the micro-world. Here again, the quantum outcomes are highly uncertain, but the law of large numbers obliges their convergence to the definite quantities we know from our everyday lives. By augmenting this description with a final boundary condition and employing the notion of "classical robustness under time-reversal" I will draw a quantitative borderline between the classical and quantum regimes. I will conclude by analyzing the role of macroscopic systems in amplifying and recording quantum outcomes.