How Quantum Contextuality disappears in the Classical Limit

TL;DR

This paper investigates how quantum contextuality, a hallmark of nonclassicality, is suppressed by environmental noise, explaining the quantum-to-classical transition through open-system dynamics.

Contribution

It provides a detailed analysis of how depolarizing noise in sequential measurements suppresses quantum contextuality, clarifying the disappearance of nonclassical correlations in the classical limit.

Findings

Depolarizing channels suppress contextual correlations in KCBS and Peres-Mermin scenarios.

Sequential measurement analysis reveals how noise leads to classicalization.

Both Schrödinger and Heisenberg pictures show the decay of contextuality under noise.

Abstract

The emergence of classicality is fundamentally driven by the interaction between a quantum system and its environment. Foundational open-system approaches, notably the Caldeira-Leggett model, successfully captured how these interactions lead to macroscopic effects like quantum dissipation and decoherence. However, these approaches often leave the precise definitions of classicality and quantumness ambiguous. In quantum information theory, this boundary is a heavily scrutinized question, and Kochen-Specker contextuality emerges as a hallmark of nonclassicality. It is therefore natural to investigate whether decoherence can actually suppress this property. Taking this path creates an apparent conundrum, once there exist two distinct manifestations of quantum contextuality: state-dependent and state-independent ones. While state-dependent contextuality naturally vanishes under state degradation, state-independent contextuality could persist for any quantum state, since it shows up even for the maximally mixed state! In this paper, we resolve this apparent paradox by analyzing sequential measurement implementations of the paradigmatic Klyachko, Can, Binicio\u{g}lu, and Shumovsky (KCBS) and Peres-Mermin prepare-and-measure scenarios under the influence of depolarizing channels. By introducing noise both prior to and in between measurements, and by analyzing the resulting sequential correlators in both the Schr\"odinger and Heisenberg pictures, we show how open-system dynamics suppress the correlations required to witness contextuality, leading to classicalization.