Recent efforts to detect non-Markovian memory have become increasingly important, motivated by the broad relevance of memory effects in quantum information processing, metrology, and thermodynamic engines. Here, we show that interferometric methods, particularly the phase shift and visibility, provide an experimentally accessible framework for probing environmental effects and witnessing non-Markovian dynamics. Specifically, suitably constructed witness operators enable the detection of non-Markovianity through measurable phase shifts in the interference pattern. Furthermore, we prove that the interferometric visibility is monotonically non-increasing under incoherent CP-divisible (Markovian) dynamics. Consequently, any revival of the optimized visibility constitutes a sufficient signature of information backflow and hence non-Markovianity. The effectiveness of the proposed phase-based and visibility approaches is illustrated for representative examples of non-Markovian dynamics. Our results offer a simple and experimentally feasible framework for probing memory effects, with potential applications in quantum sensing and noisy intermediate-scale quantum devices.
Recent efforts to detect non-Markovian memory have become increasingly important, motivated by the broad relevance of memory effects in quantum information processing, metrology, and thermodynamic engines. Here, we show that interferometric methods, particularly the phase shift and visibility, provide an experimentally accessible framework for probing environmental effects and witnessing non-Markovian dynamics. Specifically, suitably constructed witness operators enable the detection of non-Markovianity through measurable phase shifts in the interference pattern. Furthermore, we prove that the interferometric visibility is monotonically non-increasing under incoherent CP-divisible (Markovian) dynamics. Consequently, any revival of the optimized visibility constitutes a sufficient signature of information backflow and hence non-Markovianity. The effectiveness of the proposed phase-based and visibility approaches is illustrated for representative examples of non-Markovian dynamics. Our results offer a simple and experimentally feasible framework for probing memory effects, with potential applications in quantum sensing and noisy intermediate-scale quantum devices.
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 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.
Abstract The dynamics of open quantum systems and manipulation of quantum resources are both of fundamental interest in quantum physics. Here, we investigate the relation between quantum Markovianity and coherence, providing an effective way for detecting non-Markovianity based on the quantum-incoherent relative entropy of coherence ( QI QI REC). We theoretically show the relation between completely positive (CP) divisibility and the monotonic behavior of the QI QI REC. Also we implement an all-optical experiment to demonstrate that the behavior of the QI QI REC is coincident with the entanglement shared between the system and the ancilla for both Markovian and non-Markovian evolution; while other coherence-based non-Markovian information carriers violate monotonicity, even in Markovian processes. Moreover, both theoretically and experimentally, we show that non-Markovianity enhances the ability of creating coherence on an ancilla. This is the first experimental study of the relation between dynamical behavior of the QI QI REC and the phenomenon of information backflow. Our methods for detecting non-Markovianity are applicable to general quantum evolutions.
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 Jamio\l{}kowski-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.
Quantifying non-Markovianity is a fundamental problem in the theory of open quantum systems, as it is essential for exploiting environmental memory as a resource in quantum technologies. Existing resource-theoretic and operational quantifiers, however, generally require complete knowledge of the intermediate dynamical map and are therefore experimentally demanding. Here, we develop a witness-based framework for the quantification of non-Markovianity that bypasses complete reconstruction of the Choi state associated with the intermediate dynamical map. We first show that every non-Markovianity witness provides a certifiable lower bound on the geometric resource measure of non-Markovianity and identify the necessary and sufficient conditions under which this bound is tight. Motivated by the fact that non-positive-semidefinite witnesses are generally difficult to measure in real experimental scenario, we then focus on positive-semidefinite witnesses, which admit a natural implementation as positive operator valued measure (POVM) elements. We prove that every positive witness yields a certified lower bound on the Rivas--Huelga--Plenio (RHP) measure, thereby establishing a complete hierarchy connecting witness-based quantification, the RHP measure, and the geometric distance measure. Applying our framework to amplitude-damping and general Pauli dynamics, we find that the optimal positive witnesses reduce to simple Bell-parity projectors. Furthermore, we show that the resulting witness values can be obtained directly from a small number of experimentally accessible correlation measurements, thereby eliminating the need for complete Choi-state reconstruction and providing an efficient and experimentally feasible approach for the quantification of non-Markovianity in open quantum systems.
ABSTRACT: We use the divisibility approach to describe non-Markovian dynamics (memory effects) in open quantum systems coupled to an environment (reservoir). Specifically, sufficient and necessary criteria were incorporated in the energy domain that play a relevant role in dynamics of the system. In this case, we adopt the Feshbach partition in the space of (Hilbert-Liouville). On the other hand, to investigate both Markovianity and non-Markovianity, we study the divisibility of the Wigner function propagator. For this, within the framework of path integrals, we carry out an analysis of non-classical paths in phase space. Furthermore, we have used tools of topology to propose theorems intimately related to measures of non-Markovianity that are experementally accessible.
The study of open quantum systems is important for fundamental issues of quantum physics as well as for technological applications such as quantum information processing. Recent developments in this field have increased our basic understanding on how non-Markovian effects influence the dynamics of an open quantum system, paving the way to exploit memory effects for various quantum control tasks. Most often, the environment of an open system is thought to act as a sink for the system information. However, here we demonstrate experimentally that a photonic open system can exploit the information initially held by its environment. Correlations in the environmental degrees of freedom induce nonlocal memory effects where the bipartite open system displays, counterintuitively, local Markovian and global non-Markovian character. Our results also provide novel methods to protect and distribute entanglement and to experimentally quantify correlations in photonic environments.