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Register a new userDetecting Non-Markovianity via Quantified Coherence: Theory and Experiments
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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 textit{quantum-incoherent relative entropy of coherence} ($mathcal{QI}$ REC). We theoretically show the relation between completely positive (CP) divisibility and the monotonic behavior of the $mathcal{QI}$ REC. Also we implement an all-optical experiment to demonstrate that the behavior of the $mathcal{QI}$ 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, we experimentally observe 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 $mathcal{QI}$ REC and the phenomenon of information backflow. Moreover, our method for detecting non-Markovianity is applicable to general quantum evolutions.
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We provide an analysis on non-Markovian quantum evolution based on the spectral properties of dynamical maps. We introduce the dynamical analog of entanglement witness to detect non-Markovianity and we illustrate its behaviour with several instructive examples. It is shown that for a certain class of dynamical maps the shape of the body of accessible states provides a simple non-Markovianity witness.
Based on the nonincreasing property of quantum coherence via skew information under incoherent completely positive and trace-preserving maps, we propose a non-Markovianity measure for open quantum processes. As applications, by applying the proposed measure to some typical noisy channels, we find that it is equivalent to the three previous measures of non-Markovianity for phase damping and amplitude damping channels, i.e., the measures based on the quantum trace distance, dynamical divisibility, and quantum mutual information. For the random unitary channel, it is equivalent to the non-Markovianity measure based on $l_1$ norm of coherence for a class of output states and it is incompletely equivalent to the measure based on dynamical divisibility. We also use the modified Tsallis relative $alpha$ entropy of coherence to detect the non-Markovianity of dynamics of quantum open systems, the results show that the modified Tsallis relative $alpha$ entropy of coherence are more comfortable than the original Tsallis relative $alpha$ entropy of coherence for small $alpha$.
Open quantum systems exhibit a rich phenomenology, in comparison to closed quantum systems that evolve unitarily according to the Schrodinger equation. The dynamics of an open quantum system are typically classified into Markovian and non-Markovian, depending on whether the dynamics can be decomposed into valid quantum operations at any time scale. Since Markovian evolutions are easier to simulate, compared to non-Markovian dynamics, it is reasonable to assume that non-Markovianity can be employed for useful quantum-technological applications. Here, we demonstrate the usefulness of non-Markovianity for preserving correlations and coherence in quantum systems. For this, we consider a broad class of qubit evolutions, having a decoherence matrix separated from zero for large times. While any such Markovian evolution leads to an exponential loss of correlations, non-Markovianity can help to preserve correlations even in the limit $t rightarrow infty$. For covariant qubit evolutions, we also show that non-Markovianity can be used to preserve quantum coherence at all times, which is an important resource for quantum metrology. We explicitly demonstrate this effect experimentally with linear optics, by implementing the required evolution that is non-Markovian at all times.
We establish a convex resource theory of non-Markovianity under the constraint of small time intervals within the temporal evolution. We construct the free operations, free states and a generalized bona-fide measure of non-Markovianity. The framework satisfies the basic properties of a consistent resource theory. The proposed resource quantifier is lower bounded by the optimization free Rivas-Huelga-Plenio (RHP) measure of nonMarkovianity. We further define the robustness of non-Markovianity and show that it can directly be expressed as a function of the RHP measure of non-Markovianity. This enables a physical interpretation of the RHP measure.
In this paper, we study measures of quantum non-Markovianity based on the conditional mutual information. We obtain such measures by considering multiple parts of the total environment such that the conditional mutual information can be defined in this multipartite setup. The benefit of this approach is that the conditional mutual information is closely related to recovery maps and Markov chains; we also point out its relations with the change of distinguishability. We study along the way the properties of leaked information which is the conditional mutual information that can be back flowed, and we use this leaked information to show that the correlated environment is necessary for nonlocal memory effect.
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