Mixing and decoherence to nearest separable states in quantum measurements

TL;DR

This paper investigates how environment-induced decoherence in quantum measurements drives the system towards the nearest separable state, resulting in a unique final state that accurately reflects measurement outcomes without requiring environment-induced superselection.

Contribution

It demonstrates through numerical analysis that decoherence leads to a specific, unique final state approaching the nearest separable state, even without environment-induced superselection.

Findings

System-apparatus density matrix evolves towards the nearest separable state

Final state correctly reflects measurement statistics

Partial transpose remains non-positive during the process

Abstract

We illustrate through numerical results a number of features of environment-induced decoherence under a broad class of apparatus-environment interactions in quantum measurements wherein the reduced system-apparatus density matrix evolves towards the nearest separable state and, in addition, there occurs a mixing in relevant groups of apparatus microstates (see below). The resulting final state is unique and correctly embodies the measurement statistics even in the absence of environment-induced superselection because of energy differences between these groups of states. The partial transpose remains non-positive throughout the process.