Gaussian states under coarse-grained continuous variable measurements

TL;DR

This paper investigates how coarse-grained homodyne measurements affect the reconstruction of Gaussian quantum states, comparing direct covariance matrix reconstruction and maximum likelihood estimation, revealing differences from thermal reservoir decoherence models.

Contribution

It demonstrates that coarse-graining in measurements does not mimic thermal decoherence and compares two reconstruction methods, highlighting the advantages of MLE in phase-insensitive scenarios.

Findings

Coarse-graining differs from thermal reservoir effects.

MLE provides more reliable state reconstruction.

Reconstructed states' nonclassicality varies with method.

Abstract

The quantum-to-classical transition of a quantum state is a topic of great interest in fundamental and practical aspects. A coarse-graining in quantum measurement has recently been suggested as its possible account in addition to the usual decoherence model. We here investigate the reconstruction of a Gaussian state (single mode and two modes) by coarse-grained homodyne measurements. To this aim, we employ two methods, the direct reconstruction of the covariance matrix and the maximum likelihood estimation (MLE), respectively, and examine the reconstructed state under each scheme compared to the state interacting with a Gaussian (squeezed thermal) reservoir. We clearly demonstrate that the coarse-graining model, though applied equally to all quadrature amplitudes, is not compatible with the decoherence model by a thermal (phase-insensitive) reservoir. Furthermore, we compare the performance of the direct reconstruction and the MLE methods by investigating the fidelity and the nonclassicality of the reconstructed states and show that the MLE method can generally yield a more reliable reconstruction, particularly without information on a reference frame (phase of input state).