Decoherence from universal tomographic measurements

TL;DR

This paper investigates how environmental monitoring via universal tomographic measurements induces decoherence, leading to classicality emergence, with analysis based on quasiprobability distributions and Lindblad equations.

Contribution

It provides a detailed analysis of decoherence from universal measurements using two equivalent formulations and explores how decoherence timescales vary with system size.

Findings

Decoherence makes quasiprobability distributions positive, indicating classicality.

Decoherence timescale decreases with increasing Hilbert-space dimension.

Larger quantum systems decohere faster.

Abstract

The decoherence phenomenon arising from an environmental monitoring of the state of a quantum system, as opposed to monitoring of a preferred observable, is worked out in detail using two equivalent formulations, namely, repeated applications of universal tomographic measurements using positive operator-valued measures, and its continuous time unravelling from the Lindblad equation. The effect of decoherence is analysed by studying the evolution of Stratonovich-Weyl quasiprobability distributions on the state-space of the system. It is shown that decoherence makes an arbitrary-given quasiprobability distribution manifestly positive, thus modelling the emergence of classicality in some sense. The decoherence timescale, the minimum time that quasiprobability distributions of every initial state of the system become nonnegative, is shown to decrease in Hilbert-space dimension, and hence larger quantum systems decohere faster.