Characterizing non-Markovianity via quantum interferometric power

Abstract

Non-Markovian evolution in open quantum systems is often characterized in terms of the backflow of information from environment to system and is thus an important facet in investigating the performance and robustness of quantum information protocols. In this work, we explore non-Markovianity through the breakdown of monotonicity of a metrological figure of merit, called the quantum interferometric power, which is based on the minimal quantum Fisher information obtained by local unitary evolution of one part of the system, and can be interpreted as a quantifier of quantum correlations beyond entanglement. We investigate our proposed non-Markovianity indicator in two relevant examples. First, we consider the action of a single-party dephasing channel on a maximally entangled two-qubit state, by applying the Jamiołkowski-Choi isomorphism. We observe that the proposed measure is consistent with established non-Markovianity quantifiers defined using other approaches based on dynamical divisibility, distinguishability, and breakdown of monotonicity for the quantum mutual information. Further, we consider the dynamics of two-qubit Werner states, under the action of a local, single-party amplitude damping channel, and observe that the nonmonotonic evolution of the quantum interferometric power is more robust than the corresponding one for entanglement in capturing the backflow of quantum information associated with the non-Markovian process. Implications for the role of non-Markovianity in quantum metrology and possible extensions to continuous variable systems are discussed.

An Introduction to Operational Quantum Dynamics

“…From here on we omit the subscript s on the control operation A s , and assume it only acts on the system. From (33), it is clear that the superchannel is linear in the same way as E, as argued at the beginning of Sect. 2.…”

“…A measure of non-Markovianity can be defined by summing up the non-monotonicity in time [10]. Other witnesses are based on: how quantum Fisher information changes [52,33]; the detection of initial correlations [56,83]; changes to quantum correlations [53]; positivity of quantum maps [98,25]; and, most notably, witnessing the breakdown of the divisibility of a process [79]. These witnesses are turned into measures by quantifying the degree to which they witness the departure from Markov dynamics.…”

Energy backflow in strongly coupled non-Markovian continuous-variable systems

“…While the non-Markovianity measure N Q (Λ) [26] includes a maximization over all possible initial two-mode Gaussian states:…”

Role of non-Markovianity and backflow of information in the speed of quantum evolution

“…This is especially true within the quantum realm, wherein the environment has in general a major detrimental effect on the quantum features of the system and thus hinders the performance of quantum technologies [4,5]. However, when the system-environment correlation time approaches any of the time scales characterizing the system dynamics, i.e., within the so-called non-Markovian regime [6], it may happen that reservoir memory effects give rise to revivals of the quantum properties of the system, a phenomenon that is known as backflow of information from the environment to the system [7][8][9][10][11][12][13][14][15][16]. The possibility to exploit the environment itself to combat decoherence is one of the many reasons that have recently attracted tremendous interest into the characterization, detection, and quantification of non-Markovian dynamics [17][18][19][20].…”