  Memory or time-non-local effects in open quantum dynamics pose theoretical as
well as practical challenges in the understanding and control of noisy quantum
systems. While there has been a comprehensive and concerted effort towards
developing diagnostics for non-Markovian dynamics, all existing measures rely
on time-domain measurements which are typically slow and expensive as they
require averaging several runs to resolve small transient features on a broad
background, and scale unfavorably with system size and complexity. In this
work, we propose a spectroscopic measure of non-Markovianity which can detect
persistent non-Markovianity in the system steady state. In addition to being
experimentally viable, the proposed measure has a direct information theoretic
interpretation: a large value indicates the information loss per unit bandwidth
of making the Markov approximation. In the same vein, we derive a
frequency-domain quantum master equation (FD-QME) that goes beyond the standard
Born-Redfield description and retains the full memory of the state of the
reduced system. Using the FD-QME and the proposed measure, we are able to
reliably diagnose and quantify non-Markovianity in several system-environment
settings including those with environmental correlations and retardation
effects.
