Intrinsic Pointer Basis and Irreversible Classicality from Coherence Contraction

TL;DR

This paper introduces an intrinsic basis for quantum states that reveals how classical behavior emerges through coherence decay, providing a new criterion for classicality testable via interferometry.

Contribution

It defines an intrinsic reference basis and coherence measure, proving their stability and decay properties under certain open-system dynamics, advancing understanding of quantum-to-classical transition.

Findings

Quadratic coherence functional acts as a Lyapunov functional under specific dynamics.

Intrinsic coherences decay exponentially at computable rates.

IRB projectors serve as stable pointer sectors under IRB-selective evolution.

Abstract

The irreversible emergence of classical behavior from a reduced quantum description via a canonical intrinsic decomposition of the density operator is analyzed. In the intrinsic reference basis (IRB), defined for a fixed physical conjugation K (determined by measurement convention, system symmetry, or secular approximation) by diagonalizing the real symmetric part of the state, the density operator separates into a diagonal population sector and a real antisymmetric coherence sector. For the class of Markovian open-system dynamics whose Lindblad operators are diagonal in the IRB, we prove that the quadratic coherence functional is a Lyapunov functional under pure-dephasing or interaction-picture evolution, with each intrinsic coherence component decaying exponentially at a computable rate. This yields a canonical state-dependent operational classicality criterion via the normalized cohesion index, an explicit logarithmic classicalization time controlled by the slowest dephasing rate, and a demonstration that the IRB projectors emerge as dynamically stable pointer sectors under IRB-selective evolution. Suppression of intrinsic coherences is exactly equivalent to suppression of fringe visibility in the corresponding interferometric sector; for a balanced two-path setup the cohesion index coincides with the fringe visibility, making the classicality criterion directly testable with standard interferometric equipment. The approach complements environment-induced einselection: it is applicable whenever a coarse-grained reduced description is available, independently of whether the microscopic system-environment coupling is known.