Kirkwood-Dirac Quasiprobability as a Universal Framework for Quantum Measurements Across All Regimes

TL;DR

This paper establishes the Kirkwood-Dirac quasiprobability as a universal framework for quantum measurements, explaining its continuous transformation from weak to strong regimes via pointer-induced decoherence.

Contribution

It identifies pointer-induced decoherence as the universal mechanism controlling the transition of KD quasiprobability across measurement regimes.

Findings

KD quasiprobability deforms from complex weak values to real classical probabilities

Decoherence factor F(t) quantifies coherence loss and measurement strength

Framework maintains informational completeness throughout the transition

Abstract

The question of when the Kirkwood-Dirac quasiprobability serves as the most appropriate description for quantum measurements has remained unresolved, particularly across different measurement strengths. While known to generate anomalous weak values in the weak measurement regime and to reduce to classical probabilities under projective measurement, the physical mechanism governing its continuous transformation has been lacking. Here we demonstrate that the KD quasiprobability provides a general framework for all measurement regimes by identifying pointer-induced decoherence as the universal mechanism controlling this transition. We show that the decoherence factor F(t) simultaneously quantifies the loss of quantum coherence and interpolates the measurement strength from weak to strong. Within this framework, the KD quasiprobability naturally deforms from its full complex form-governing weak values-to the real, non-negative Wigner formula describing projective measurements, while maintaining informational completeness throughout the transition. Our work resolves the fundamental question of the KD distribution's applicability by establishing it as the universal framework that seamlessly connects all quantum measurement regimes through a physically transparent decoherence pathway.