[Paper Review] Weak measurement, projective measurement and quantum-to-classical transitions in electron-photon interactions

Yiming Pan, Eliahu Cohen+4 more|arXiv (Cornell University)|Oct 24, 2019

Quantum Information and Cryptography25 references4 citations

TL;DR

This paper introduces a measurement-based framework linking projective and weak measurements in electron-photon interactions, showing that classical electron behavior—like point-particle acceleration—emerges as an amplified weak value. A universal decay factor exp(−Γ²/2), where Γ is the ratio of electron wavepacket size to optical wavelength, quantifies the quantum-to-classical transition across measurement regimes.

ABSTRACT

How does the quantum-to-classical transition of measurement occur? This question is vital for both foundations and applications of quantum mechanics. We developed a new measurement-based framework for characterizing the classical and quantum free electron-photon interactions. We first analyze the transition from projective measurement to weak measurement in generic light-matter interactions, and show that any classical electron-laser-beam interaction can be represented as an outcome of a weak measurement. In particular, the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement. A universal decay factor $\exp(-\Gamma^2/2)$, quantifies the measurement regimes and their transition from quantum to classical, where $\Gamma$ corresponds to the ratio between the electron wavepacket size and the optical wavelength. This presentation of the measurement transition from projective to weak sheds new light on the transition from quantum-to-classical electrodynamics, enabling to employ the very essence of wave-particle duality in quantum measurement for exploring and applying a variety of quantum and classical types of electron-photon interactions.

Motivation & Objective

• To clarify the mechanism of the quantum-to-classical transition in light-matter interactions.
• To bridge the conceptual and quantitative gap between projective and weak measurements in electron-photon systems.
• To demonstrate that classical electron-laser interactions are manifestations of weak measurement outcomes.
• To quantify the measurement regime transition using a universal decay factor exp(−Γ²/2).
• To unify quantum and classical descriptions of electron-photon interactions through wave-particle duality in measurement.

Proposed method

• Analyzes the transition from projective to weak measurement in generic light-matter interactions.
• Introduces the parameter Γ = (electron wavepacket size) / (optical wavelength) as a key control variable.
• Derives the universal decay factor exp(−Γ²/2) to quantify measurement regime transitions.
• Models classical electron-laser interactions as resulting from weak measurement outcomes.
• Uses weak value amplification to explain the emergence of classical point-particle acceleration.
• Applies wave-particle duality principles to unify quantum and classical descriptions of electron-photon dynamics.

Experimental results

Research questions

• RQ1 How does the transition from projective to weak measurement manifest in electron-photon interactions?
• RQ2 What determines the boundary between quantum and classical behavior in electron-laser systems?
• RQ3 Can classical electron acceleration be understood as an amplified weak value?
• RQ4 How does the ratio of electron wavepacket size to optical wavelength influence measurement regimes?
• RQ5 What universal factor governs the transition from quantum to classical electrodynamics in these systems?

Key findings

• Classical electron-laser interactions are shown to be equivalent to outcomes of weak measurement processes.
• The appearance of classical point-particle acceleration arises from amplified weak values in the weak measurement regime.
• The universal decay factor exp(−Γ²/2) quantitatively characterizes the transition from quantum to classical measurement regimes.
• The parameter Γ, defined as the ratio of electron wavepacket size to optical wavelength, determines the measurement regime.
• The framework provides a unified description of both quantum and classical electron-photon interactions via measurement theory.
• The results establish a direct link between wave-particle duality and the emergence of classical behavior in quantum measurement.