Quantum filtering of a thermal master equation with purified reservoir

TL;DR

This paper explores how monitoring a purified environment in a quantum system at finite temperature can enhance quantum filtering, leading to improved squeezing and entanglement compared to traditional methods.

Contribution

It introduces a class of unravellings based on environmental purification, demonstrating how access to the bath's purification enhances quantum filtering performance.

Findings

Full bath purification access yields maximal steady-state squeezing.

Direct detection of the environment is less effective than purified bath monitoring.

Access to bath purification improves filtering outcomes in squeezing and entanglement.

Abstract

We consider a system subject to a quantum optical master equation at finite temperature and study a class of conditional dynamics obtained by monitoring its totally or partially purified environment. More specifically, drawing from the notion that the thermal state of the environment may be regarded as the local state of a lossy and noisy two-mode squeezed state, we consider conditional dynamics ("unravellings") resulting from the homodyne detection of the two modes of such a state. Thus, we identify a class of unravellings parametrised by the loss rate suffered by the environmental two-mode state, which interpolate between direct detection of the environmental mode alone (occurring for total loss, whereby no correlation between the two environmental modes is left) and full access to the purification of the bath (occurring when no loss is acting and the two-mode state of the environment is pure). We hence show that, while direct detection of the bath is not able to reach the maximal steady-state squeezing allowed by general-dyne unravellings, such optimal values can be obtained when a fully purified bath is accessible. More generally we show that, within our framework, any degree of access to the bath purification improves the performance of filtering protocols in terms of achievable squeezing and entanglement.