Gaussian interferometric power as a measure of continuous variable non-Markovianity

TL;DR

This paper explores how Gaussian interferometric power can serve as an operational tool to detect and quantify non-Markovian dynamics in continuous variable Gaussian quantum channels, linking quantum dynamics with optical interferometry.

Contribution

It introduces a novel method using Gaussian interferometric power to witness and measure non-Markovianity in continuous variable systems, including nonentangled probes.

Findings

Gaussian interferometric power decreases monotonically under Markovian dynamics

Breakdown of monotonicity indicates non-Markovian behavior

Nonentangled probes can effectively witness non-Markovianity

Abstract

We investigate the non-Markovianity of continuous variable Gaussian quantum channels through the evolution of an operational metrological quantifier, namely the Gaussian interferometric power, which captures the minimal precision that can be achieved using bipartite Gaussian probes in a black-box phase estimation setup, where the phase shift generator is \emph{a priori} unknown. We observe that the monotonicity of the Gaussian interferometric power under the action of local Gaussian quantum channels on the ancillary arm of the bipartite probes is a natural indicator of Markovian dynamics; consequently, its breakdown for specific maps can be used to construct a witness and an effective quantifier of non-Markovianity. In our work, we consider two paradigmatic Gaussian models, the damping master equation and the quantum Brownian motion, and identify analytically and numerically the parameter regimes that give rise to non-Markovian dynamics. We then quantify the degree of non-Markovianity of the channels in terms of Gaussian interferometric power, showing in particular that even nonentangled probes can be useful to witness non-Markovianity. This establishes an interesting link between the dynamics of bipartite continuous variable open systems and their potential for optical interferometry. The results are an important supplement to the recent research on characterization of non-Markovianity in continuous variable systems.