The description of how different quantum features, such as non-Markovianity and quantumness, interact in quantum channels is an important step in designing and managing quantum systems. Here, we look at three non-Markovian dephasing channels: pink, brown, and static noise. We investigate and evaluate various measures of non-Markovianity in these channels. Indeed, the proposed measurements include trace norm, entropy, and quantum capacity. We investigate the effect of non-Markovianity on the quantum nature of these channels. Our results show that increasing the degree of non-Markovianity in the suggested channels does not always improve the channel's quantumness. Furthermore, given the aforementioned quantum channels, the l2 norm of quantum coherence and mixedness satisfies the trade-off relation, which is critical for understanding how quantum resources and noise interact in open quantum systems.
The description of how different quantum features, such as non-Markovianity and quantumness, interact in quantum channels is an important step in designing and managing quantum systems. Here, we look at three non-Markovian dephasing channels: pink, brown, and static noise. We investigate and evaluate various measures of non-Markovianity in these channels. Indeed, the proposed measurements include trace norm, entropy, and quantum capacity. We investigate the effect of non-Markovianity on the quantum nature of these channels. Our results show that increasing the degree of non-Markovianity in the suggested channels does not always improve the channel's quantumness. Furthermore, given the aforementioned quantum channels, the l2 norm of quantum coherence and mixedness satisfies the trade-off relation, which is critical for understanding how quantum resources and noise interact in open quantum systems.
We address the non-Markovian character of quantum maps describing the interaction of a qubit with a random classical field. In particular, we evaluate trace- and capacity-based non-Markovianity measures for two relevant classes of environments showing non-Gaussian fluctuations, described respectively by random telegraph noise and colored noise with spectra of the the form $1/{f}^{\ensuremath{\alpha}}$. We analyze the dynamics of both the trace distance and the quantum capacity, and show that the behavior of non-Markovianity based on both measures is qualitatively similar. Our results show that environments with a spectrum that contains a relevant low-frequency contribution are generally non-Markovian. We also find that the non-Markovianity of colored environments decreases when the number of fluctuators realizing the environment increases.
We propose an approach to measuring non-Markovianity of an open two-level system from quantum coherence perspective including l1 norm of coherence and quantum relative entropy of coherence, and derive corresponding non-Markovian conditions. Further, as a particular application, non-Markovian conditions of an open two-level system undergoing phase damping channel, random unitary channel and amplitude damping channel, respectively are investigated. Specifically speaking, for the three channels we obtain non-Markovian conditions based on l1 norm of coherence at any initial state of system, and find that non-Markovian conditions are the same as the conditions of other measurements, i.e., information back-flow, divisibility and quantum mutual entropy for the phase damping channel and amplitude damping channel, but non-Markovian conditions new and different from the conditions of other measurements for random unitary channel. On the other hand, for phase damping channel we obtain non-Markovian conditions based on quantum relative entropy of coherence at any initial state of system, which are the same as the conditions of other measures, i.e., information back-flow, divisibility and quantum mutual entropy. However, for the random unitary channel and amplitude damping channel we obtain non-Markovian conditions at maximally coherent state of system.
Quantum computation and quantum communication are two of the most promising future applications of quantum mechanics. Since the information carriers used in both of them are essentially open quantum systems it is necessary to understand both quantum information theory and the theory of open quantum systems in order to investigate realistic implementations of such quantum technologies. In this thesis we consider the theory of open quantum systems from a quantum information theory perspective. The thesis is divided into two parts: review of the literature and original research. In the review of literature we present some important definitions and known results of open quantum systems and quantum information theory. We present the definitions of trace distance, two channel capacities and superdense coding capacity and give a reasoning why they can be used to represent the transmission efficiency of a communication channel. We also show derivations of some properties useful to link completely positive and trace preserving maps to trace distance and channel capacities. With the help of these properties we construct three measures of non-Markovianity and explain why they detect non-Markovianity. In the original research part of the thesis we study the non-Markovian dynamics in an experimentally realized quantum optical set-up. For general one-qubit dephasing channels we calculate the explicit forms of the two channel capacities and the superdense coding capacity. For the general two-qubit dephasing channel with uncorrelated local noises we calculate the explicit forms of the quantum capacity and the mutual information of a four-letter encoding. By using the dynamics in the experimental implementation as a set of specific dephasing channels we also calculate and compare the measures in one- and two-qubit dephasing channels and study the options of manipulating the environment to achieve revivals and higher transmission rates in superdense coding protocol with dephasing noise. Kvanttilaskenta ja kvanttikommunikaatio ovat kaksi puhutuimmista tulevaisuuden kvanttimekaniikan käytännön sovelluksista. Koska molemmissa näistä informaatio koodataan systeemeihin, jotka ovat oleellisesti avoimia kvanttisysteemejä, sekä kvantti-informaatioteorian, että avointen kvanttisysteemien tuntemus on välttämätöntä. Tässä tutkielmassa käsittelemme avointen kvanttisysteemien teoriaa kvantti-informaatioteorian näkökulmasta. Tutkielma on jaettu kahteen osioon: kirjallisuuskatsaukseen ja omaan tutkimukseen. Kirjallisuuskatsauksessa esitämme joitakin avointen kvanttisysteemien ja kvantti-informaatioteorian tärkeitä määritelmiä ja tunnettuja tuloksia. Esitämme jälkietäisyyden, kahden kanavakapasiteetin ja superdense coding -kapasiteetin määritelmät ja esitämme perustelun sille, miksi niitä voidaan käyttää kuvaamaan kommunikointikanavan lähetystehokkuutta. Näytämme myös todistukset kahdelle ominaisuudelle, jotka liittävät täyspositiiviset ja jäljensäilyttävät kuvaukset jälkietäisyyteen ja kanavakapasiteetteihin. Näiden ominaisuuksien avulla konstruoimme kolme epä-Markovisuusmittaa ja perustelemme, miksi ne havaitsevat dynamiikan epä-Markovisuutta. Oman tutkimuksen osiossa tutkimme epä-Markovista dynamiikkaa kokeellisesti toteutetussa kvanttioptisessa mittausjärjestelyssä. Yleisen yhden qubitin dephasing-kanavan tapauksessa laskemme molempien kanavakapasiteettien ja superdense coding -kapasiteetin eksplisiittiset muodot. Yleisen kahden qubitin korreloimattomien ympäristöjen dephasing-kanavan tapauksessa laskemme yhteisen informaation lausekkeen nelikirjaimisessa koodauksessa ja kvanttikanavakapasiteetin. Käyttämällä kokeellisen mittajärjestelyn dynamiikkoja esimerkki dephasing-kanavina me myös laskemme konstruoitujen epä-Markovisuusmittojen arvot ja vertailemme niitä yksi- ja kaksi-qubitti-dephasing-kanavissa. Lisäksi käyttäen kokeellisia esimerkkikanavia tutkimme, kuinka ympäristöä manipuloimalla superdense coding –skeemassa voidaan saada yhteinen informaatio ajoittain kasvamaan tai saavuttaa kaikenkaikkiaan korkeampi lähetystehokkuus.
Abstract 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 entropy of coherence to detect the non-Markovianity of dynamics of quantum open systems, the results show that the modified Tsallis relative entropy of coherence are more comfortable than the original Tsallis relative entropy of coherence for small .
The non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment, and it is thought to be a resource for various quantum information tasks. We have investigated the non-Markovianity of the dynamics of a two-state system driven by continuous time random walk-type noise, which can be Markovian or non-Markovian depending on its residence time distribution parameters. Exact analytical expressions for the distinguishability as well as the trace distance and entropy-based non-Markovianity measures are obtained and used to investigate the interplay between the non-Markovianity of the noise and that of dynamics. Our results show that, in many cases, the dynamics are also non-Markovian when the noise is non-Markovian. However, it is possible for Markovian noise to cause non-Markovian dynamics and for non-Markovian noise to cause Markovian dynamics but only for certain parameter values.
The uncertainty principle limits the ability for observer to precisely measure two incompatible observables, and plays a crucial role in quantum precision measurement in the quantum information science. When quantum systems interact with their surroundings, they inevitably result in decoherence, which increases the uncertainty of the system. In the process of quantum information processing, the effective regulation of uncertainty becomes a key problem that needs to be solved. In this work, we investigate the quantum-memory-assisted entropic uncertainty relation of a two-qubit system under correlated channels with dephasing colored noise. We demonstrate that it is possible to control the entropic uncertainty, U, and its lower bound, Ub, by combining correlations between successive uses of channels and the non-Markovianity of the dynamical evolution. Firstly, the evolutionary characteristics of the trace distance are employed to distinguish between Markovianity and non-Markovianity of the channel. Subsequently, the system is selected to be either a maximally entangled state or separated state initially. By adjusting the strength η of the correlations, we find that with the increase of η, the entropic uncertainty and its lower bound decrease. Especially, if the channel is fully correlated (η = 1), the entropic uncertainty and its lower bound remain constant under the channel, indicating that decoherence is completely suppressed. A comparison of Markovian channel with non-Markovian channel reveals that the entropic uncertainty and its lower bound exhibit oscillatory behaviour under non-Markovian channels. The combination of correlations and non-Markovianity of the channel demonstrates that the entropic uncertainty and its lower bound can be reduced under fully correlated channels where the non-Markovianity has no effect. This is because fully correlated channels suppress decoherence to a greatest extent. Under partially correlated channels, the combination of correlations and non-Markovianity can more effectively reduce the entropic uncertainty and its lower bound. Under such channels, correlations of the channel reduce the entropic uncertainty and its lower bound during the whole evolution, while the non-Markovianity contributes to their oscillations and reduce them in some specific time. Furthermore, the results show that the entropic uncertainty and its lower bound reach steady values that depend only on the strength of the correlations after long-time evolution. In other words, the stronger the correlations, the lower the entropy uncertainty and its lower bound of steady states will be. Finally, we analyse the physical nature of the decrease of the entropic uncertainty and its lower bound, and it is found that the decrease of the entropic uncertainty and its lower bound originate from the increase of the quantum correlations in the system.