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Register a new userNon-markovianity and bound states in quantum walks with a phase impurity
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Bur\\c{c}in Danac{\\i}
Publication date
2018
fields
Physics
and research's language is
English
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We study a quantum walker on a one-dimensional lattice with a single defect site characterized by a phase. The spread and localization of discrete-time quantum walks starting at the impurity site are affected by the appearance of bound states and their reflection symmetry. We quantify the localization in terms of an effective localization length averaged over all eigenstates and an effective participation ratio after time evolution averaged over all initial states. We observe that the reduced coin system dynamics undergoes oscillations in the long-time limit, the frequencies of which are related to the unitary sublattice operator and the bound state quasi-energy differences. The oscillations give rise to non-Markovian evolution, which we quantify using the trace distance and entanglement based measures of non-Markovianity. Indeed, we reveal that the degree of the non-Markovian behavior is closely related to the emergence of bound states due to the phase impurity. We also show that the considered measures give qualitatively different results depending on the number and symmetries of supported bound states. Finally, comparing localization and non-Markovianity measures, we demonstrate that the degree of non-Markovianity becomes maximum when the walker is most localized in position space.
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Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develop a general description of such a quantum walk and show how to map it into a standard one with orthogonal states, thereby making available all the tools developed for the latter. This enables a variety of experiments, which can be implemented with smaller step sizes and more steps. Tuning the non-orthogonality allows for an easy preparation of extended states such as momentum eigenstates, which travel at a well-defined speed with low dispersion. We introduce a method to adjust their velocity by momentum shifts, which allows to investigate intriguing effects such as the analog of Bloch oscillations.
Recently remarkable progress in quantum technology has been witnessed. In view of this it is important to investigate an open quantum system as a model of such quantum devices. Quantum devices often require extreme conditions such as very low temperature for the devices to operate. Dynamics can be non-Markovian in such a situation in contrast with Markovian dynamics in high temperature regime. This observation necessitates us to investigate a non-Markovian open quantum system, both theoretically and experimentally. In this paper, we report two important results: 1) Exact solution of a simple but non-trivial theoretical model and 2) demonstration of this model by NMR experiments, where non-Markovianity is continuously controllable. We observe qualitative agreement between theory and experiment.
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.
Detuned systems can spontaneously achieve a synchronous dynamics and display robust quantum correlations in different local and global dissipation regimes. Beyond the Markovian limit, information backflow from the environment becomes a crucial mechanism whose interplay with spontaneous synchronization is unknown. Considering a model of two coupled qubits, one of which interacts with a dissipative environment, we show that non-Markovianity is highly detrimental for the emergence of synchronization, for the latter can be delayed and hindered because of the presence of information backflow. The results are obtained considering both a master equation approach and a collision model based on repeated interactions, which represents a very versatile tool to tailor the desired kind of environment.
To quantify non-Markovianity of tripartite quantum states from an operational viewpoint, we introduce a class $Omega^*$ of operations performed by three distant parties. A tripartite quantum state is a free state under $Omega^*$ if and only if it is a quantum Markov chain. We introduce a function of tripartite quantum states that we call the non-Markovianity of formation, and prove that it is a faithful measure of non-Markovianity, which is continuous and monotonically nonincreasing under a subclass $Omega$ of $Omega^*$. We consider a task in which the three parties generate a non-Markov state from scratch by operations in $Omega$, assisted with quantum communication from the third party to the others, which does not belong to $Omega$. We prove that the minimum cost of quantum communication required therein is asymptotically equal to the regularized non-Markovianity of formation. Based on this result, we provide a direct operational meaning to a measure of bipartite entanglement called the c-squashed entanglement.
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